Law firms cannot act for a party they've acted against (and vice-versa) without a waiver from their existing client. It can be costly for a firm if they make that mistake.

They can, however, take on competing companies for a single action if they all agree. It's probably best if the firm didn't have a prior relationship with any of them.

(Not a lawyer but I am a software developer who's built a legal conflict of interest search system)