diff --git a/evm/src/all_stark.rs b/evm/src/all_stark.rs
index 0448ab52..b5c65fec 100644
--- a/evm/src/all_stark.rs
+++ b/evm/src/all_stark.rs
@@ -107,8 +107,8 @@ mod tests {
         keccak_trace[5].values[..].copy_from_slice(&vs1);
 
         let cross_table_lookups = vec![CrossTableLookup {
-            looking_table: Table::Cpu,
-            looking_columns: vec![2, 4],
+            looking_tables: vec![Table::Cpu],
+            looking_columns: vec![vec![2, 4]],
             looked_table: Table::Keccak,
             looked_columns: vec![3, 5],
             default: vec![F::ONE; 2],
diff --git a/evm/src/cross_table_lookup.rs b/evm/src/cross_table_lookup.rs
index d29958be..f8d3e6d5 100644
--- a/evm/src/cross_table_lookup.rs
+++ b/evm/src/cross_table_lookup.rs
@@ -1,4 +1,5 @@
 use anyhow::{ensure, Result};
+use itertools::izip;
 use plonky2::field::extension_field::{Extendable, FieldExtension};
 use plonky2::field::field_types::Field;
 use plonky2::field::packed_field::PackedField;
@@ -22,8 +23,8 @@ use crate::vars::{StarkEvaluationTargets, StarkEvaluationVars};
 
 #[derive(Clone)]
 pub struct CrossTableLookup<F: Field> {
-    pub looking_table: Table,
-    pub looking_columns: Vec<usize>,
+    pub looking_tables: Vec<Table>,
+    pub looking_columns: Vec<Vec<usize>>,
     pub looked_table: Table,
     pub looked_columns: Vec<usize>,
     pub default: Vec<F>,
@@ -31,15 +32,18 @@ pub struct CrossTableLookup<F: Field> {
 
 impl<F: Field> CrossTableLookup<F> {
     pub fn new(
-        looking_table: Table,
-        looking_columns: Vec<usize>,
+        looking_tables: Vec<Table>,
+        looking_columns: Vec<Vec<usize>>,
         looked_table: Table,
         looked_columns: Vec<usize>,
         default: Vec<F>,
     ) -> Self {
-        assert_eq!(looking_columns.len(), looked_columns.len());
+        assert_eq!(looking_tables.len(), looking_columns.len());
+        assert!(looking_columns
+            .iter()
+            .all(|cols| cols.len() == looked_columns.len()));
         Self {
-            looking_table,
+            looking_tables,
             looking_columns,
             looked_table,
             looked_columns,
@@ -87,7 +91,7 @@ pub fn cross_table_lookup_data<F: RichField, C: GenericConfig<D, F = F>, const D
     let challenges = get_grand_product_challenge_set(challenger, config.num_challenges);
     let mut ctl_data_per_table = vec![CtlData::new(challenges.clone()); trace_poly_values.len()];
     for CrossTableLookup {
-        looking_table,
+        looking_tables,
         looking_columns,
         looked_table,
         looked_columns,
@@ -95,11 +99,13 @@ pub fn cross_table_lookup_data<F: RichField, C: GenericConfig<D, F = F>, const D
     } in cross_table_lookups
     {
         for &challenge in &challenges.challenges {
-            let z_looking = partial_products(
-                &trace_poly_values[*looking_table as usize],
-                looking_columns,
-                challenge,
-            );
+            let zs_looking = looking_tables
+                .iter()
+                .zip(looking_columns)
+                .map(|(table, columns)| {
+                    partial_products(&trace_poly_values[*table as usize], columns, challenge)
+                })
+                .collect::<Vec<_>>();
             let z_looked = partial_products(
                 &trace_poly_values[*looked_table as usize],
                 looked_columns,
@@ -107,17 +113,25 @@ pub fn cross_table_lookup_data<F: RichField, C: GenericConfig<D, F = F>, const D
             );
 
             debug_assert_eq!(
-                *z_looking.values.last().unwrap(),
+                zs_looking
+                    .iter()
+                    .map(|z| *z.values.last().unwrap())
+                    .product::<F>(),
                 *z_looked.values.last().unwrap()
                     * challenge.combine(default).exp_u64(
-                        trace_poly_values[*looking_table as usize][0].len() as u64
+                        looking_tables
+                            .iter()
+                            .map(|table| trace_poly_values[*table as usize][0].len() as u64)
+                            .sum::<u64>()
                             - trace_poly_values[*looked_table as usize][0].len() as u64
                     )
             );
 
-            ctl_data_per_table[*looking_table as usize]
-                .zs_columns
-                .push((z_looking, looking_columns.clone()));
+            for (table, columns, z) in izip!(looking_tables, looking_columns, zs_looking) {
+                ctl_data_per_table[*table as usize]
+                    .zs_columns
+                    .push((z, columns.clone()));
+            }
             ctl_data_per_table[*looked_table as usize]
                 .zs_columns
                 .push((z_looked, looked_columns.clone()));
@@ -177,7 +191,7 @@ impl<'a, F: RichField + Extendable<D>, const D: usize>
 
         let mut ctl_vars_per_table = vec![vec![]; proofs.len()];
         for CrossTableLookup {
-            looking_table,
+            looking_tables,
             looking_columns,
             looked_table,
             looked_columns,
@@ -185,13 +199,15 @@ impl<'a, F: RichField + Extendable<D>, const D: usize>
         } in cross_table_lookups
         {
             for &challenges in &ctl_challenges.challenges {
-                let (looking_z, looking_z_next) = ctl_zs[*looking_table as usize].next().unwrap();
-                ctl_vars_per_table[*looking_table as usize].push(Self {
-                    local_z: *looking_z,
-                    next_z: *looking_z_next,
-                    challenges,
-                    columns: looking_columns,
-                });
+                for (table, columns) in looking_tables.iter().zip(looking_columns) {
+                    let (looking_z, looking_z_next) = ctl_zs[*table as usize].next().unwrap();
+                    ctl_vars_per_table[*table as usize].push(Self {
+                        local_z: *looking_z,
+                        next_z: *looking_z_next,
+                        challenges,
+                        columns,
+                    });
+                }
 
                 let (looked_z, looked_z_next) = ctl_zs[*looked_table as usize].next().unwrap();
                 ctl_vars_per_table[*looked_table as usize].push(Self {
@@ -262,7 +278,7 @@ impl<'a, const D: usize> CtlCheckVarsTarget<'a, D> {
 
         let mut ctl_vars_per_table = vec![vec![]; proofs.len()];
         for CrossTableLookup {
-            looking_table,
+            looking_tables,
             looking_columns,
             looked_table,
             looked_columns,
@@ -270,13 +286,15 @@ impl<'a, const D: usize> CtlCheckVarsTarget<'a, D> {
         } in cross_table_lookups
         {
             for &challenges in &ctl_challenges.challenges {
-                let (looking_z, looking_z_next) = ctl_zs[*looking_table as usize].next().unwrap();
-                ctl_vars_per_table[*looking_table as usize].push(Self {
-                    local_z: *looking_z,
-                    next_z: *looking_z_next,
-                    challenges,
-                    columns: looking_columns,
-                });
+                for (table, columns) in looking_tables.iter().zip(looking_columns) {
+                    let (looking_z, looking_z_next) = ctl_zs[*table as usize].next().unwrap();
+                    ctl_vars_per_table[*table as usize].push(Self {
+                        local_z: *looking_z,
+                        next_z: *looking_z_next,
+                        challenges,
+                        columns,
+                    });
+                }
 
                 let (looked_z, looked_z_next) = ctl_zs[*looked_table as usize].next().unwrap();
                 ctl_vars_per_table[*looked_table as usize].push(Self {
@@ -354,22 +372,29 @@ pub(crate) fn verify_cross_table_lookups<
     for (
         i,
         CrossTableLookup {
-            looking_table,
+            looking_tables,
             looked_table,
             default,
             ..
         },
     ) in cross_table_lookups.into_iter().enumerate()
     {
-        let looking_degree = 1 << degrees_bits[looking_table as usize];
+        let looking_degrees_sum = looking_tables
+            .iter()
+            .map(|&table| 1 << degrees_bits[table as usize])
+            .sum::<u64>();
         let looked_degree = 1 << degrees_bits[looked_table as usize];
-        let looking_z = *ctl_zs_openings[looking_table as usize].next().unwrap();
+        let looking_zs_prod = looking_tables
+            .into_iter()
+            .map(|table| *ctl_zs_openings[table as usize].next().unwrap())
+            .product::<F>();
         let looked_z = *ctl_zs_openings[looked_table as usize].next().unwrap();
         let challenge = challenges.challenges[i % config.num_challenges];
         let combined_default = challenge.combine(default.iter());
 
         ensure!(
-            looking_z == looked_z * combined_default.exp_u64(looking_degree - looked_degree),
+            looking_zs_prod
+                == looked_z * combined_default.exp_u64(looking_degrees_sum - looked_degree),
             "Cross-table lookup verification failed."
         );
     }
@@ -399,16 +424,23 @@ pub(crate) fn verify_cross_table_lookups_circuit<
     for (
         i,
         CrossTableLookup {
-            looking_table,
+            looking_tables,
             looked_table,
             default,
             ..
         },
     ) in cross_table_lookups.into_iter().enumerate()
     {
-        let looking_degree = 1 << degrees_bits[looking_table as usize];
+        let looking_degrees_sum = looking_tables
+            .iter()
+            .map(|&table| 1 << degrees_bits[table as usize])
+            .sum::<u64>();
         let looked_degree = 1 << degrees_bits[looked_table as usize];
-        let looking_z = *ctl_zs_openings[looking_table as usize].next().unwrap();
+        let looking_zs_prod = builder.mul_many(
+            looking_tables
+                .into_iter()
+                .map(|table| *ctl_zs_openings[table as usize].next().unwrap()),
+        );
         let looked_z = *ctl_zs_openings[looked_table as usize].next().unwrap();
         let challenge = challenges.challenges[i % inner_config.num_challenges];
         let default = default
@@ -417,8 +449,8 @@ pub(crate) fn verify_cross_table_lookups_circuit<
             .collect::<Vec<_>>();
         let combined_default = challenge.combine_base_circuit(builder, &default);
 
-        let pad = builder.exp_u64(combined_default, looking_degree - looked_degree);
+        let pad = builder.exp_u64(combined_default, looking_degrees_sum - looked_degree);
         let padded_looked_z = builder.mul(looked_z, pad);
-        builder.connect(looking_z, padded_looked_z);
+        builder.connect(looking_zs_prod, padded_looked_z);
     }
 }
diff --git a/plonky2/src/gadgets/arithmetic.rs b/plonky2/src/gadgets/arithmetic.rs
index fe6f116d..ad587a49 100644
--- a/plonky2/src/gadgets/arithmetic.rs
+++ b/plonky2/src/gadgets/arithmetic.rs
@@ -25,7 +25,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
 
     /// Computes `x^3`.
     pub fn cube(&mut self, x: Target) -> Target {
-        self.mul_many(&[x, x, x])
+        self.mul_many([x, x, x])
     }
 
     /// Computes `const_0 * multiplicand_0 * multiplicand_1 + const_1 * addend`.
@@ -206,12 +206,16 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     }
 
     /// Multiply `n` `Target`s.
-    pub fn mul_many(&mut self, terms: &[Target]) -> Target {
-        terms
-            .iter()
-            .copied()
-            .reduce(|acc, t| self.mul(acc, t))
-            .unwrap_or_else(|| self.one())
+    pub fn mul_many<T>(&mut self, terms: impl IntoIterator<Item = T>) -> Target
+    where
+        T: Borrow<Target>,
+    {
+        let mut iter = terms.into_iter();
+        if let Some(first) = iter.next() {
+            iter.fold(*first.borrow(), |acc, t| self.mul(acc, *t.borrow()))
+        } else {
+            self.one()
+        }
     }
 
     /// Exponentiate `base` to the power of `2^power_log`.