Parler is suing Amazon Web Services alleging violation of the Sherman Anti-Trust Act, breach of contract, and tortuous interference with business. IANAL, but it seems to me that this is exactly the approach that is most likely to be successful against Big Tech. If I read the complaint correctly, Parler is alleging that AWS effectively conspired with Twitter to silence Parler because it would be mutually beneficial for Amazon and Twitter.
Here’s the complaint.
Parler is asking for an injunction requiring AWS to restore their service pending the outcome of the case and for treble damages under the Sherman Anti-Trust Act.