Parler, Trump, Et Al: State First Amendment Rights And PruneYard Shopping Center v Robins

In 1980, The US Supreme Court ruled that that the State of California Constitution's first amendment rights can go beyond the rights provided by the US Constitution, (PruneYard Shopping Center v Robins). The US Supreme Court upheld a California court decision that a privately owned shopping mall open to the public must allow, under California state first amendment rights, the distribution of political literature and the solicitation of signatures for a petition by a group of students, despite mall rules that prohibited such activity. 

Other states, besides California, have free speech protection rights in their constitutions that are more expansive and protective of speech than the US Constitution. Twitter, Facebook, Apple, Google and numerous other technology firms are headquartered in California and subject to California laws and constitution. 

Can Parler successfully sue the technology companies in California court that have removed its platform from their services? Could Parler get an immediate temporary restraining order in California stopping the removal of Parler?