In an escalation of Elon Musk’s fractured relationship with President Donald Trump and his Republican allies, the Tesla CEO has floated the idea of starting a new political party to rival the two-party system.

Elon Musk’s bitter falling-out with President Trump could be costly for Tesla. As long as he is persona non grata in the Trump administration, Mr. Musk, the chief executive of Tesla, will struggle to persuade Republicans not to gut climate policies worth billions of dollars to the electric car and battery company.

Musk attacked Trump directly over his signature spending bill for the first time Thursday, sparking an explosive back-and-forth.