Elon Musk makes $43 Billion offer for private buyout of Twitter

Yep, the case law allows them to keep those cases but the appearance of a conflict is supposed to be grounds for recusal. The reality is that really depends on the Judge whether they will do it or whether the upper court will "suggest" they do it. And sometimes they do it without even telling anyone why if they don't feel like dealing with the case or don't like dealing with one of the lawyers in the case.

Judge recused in the X case

https://www.courtlistener.com/docket/69017972/10/x-corp-v-world-federation-of-advertisers/