What size drain is required for a washing machine?

You're correct, the requirement for washing machine drain is 2".

To determine if you have enough drain capacity for an additional machine, you need to consult the Uniform Plumbing Code's Drainage Fixture Unit values and ensure the total fixtures don't exceed the capacity of the drain for your laundry room (or plan an upgrade.)

These tables should help get you started:

• Fixture values https://www.engineeringtoolbox.com/drainage-fixture-unit-values-d_1077.html
• Drain capacity per pipe size in stacks & branches https://www.engineeringtoolbox.com/drainage-fixture-units-piping-load-d_1078.html