There is no limit. Some might say this is bundling, but I seriously doubt the wires are tightly grouped together for more than 24″ in this instance. As many as you can without damaging the jackets of the cables. You need to address derating issues when stuffing holes with cables.

How many Romex Can you bundle together?

There is no limit. Some might say this is bundling, but I seriously doubt the wires are tightly grouped together for more than 24″ in this instance. As many as you can without damaging the jackets of the cables. You need to address derating issues when stuffing holes with cables.

Is it OK to zip tie Romex together?

Yes you can. But allowing natural air cooling is important so zip tying a bundle of cables together may mean the inside cables run hot so cables should be tied together in a manner to allow adequate cooling by natural air flow.