WASHINGTON—Steve Bannon’s war on the GOP establishment seems to have petered out, but the party is still roiling with primary fights and fundraising woes that hang over its effort to hold or expand its Senate majority.

In Nevada, Sen. Dean Heller and allies are pouring money into ads against his primary opponent, Danny Tarkanian. In Arizona, a three-way primary is pitting party leaders’ favorite against two GOP outsiders. In Mississippi, a tea-party hero is weighing another anti-establishment Senate run.

And just when the party thought the field was set in Tennessee, GOP Sen. Bob Corker is reconsidering his decision not to run for re-election, his spokeswoman said.

Mr. Bannon abruptly lost political standing after a book quoted him saying negative things about President Donald Trump’s children, and mainstream GOP leaders hoped that ended one of their biggest headaches of the midterm elections: Mr. Bannon’s vow to back challengers to Senate Republicans he deemed insufficiently loyal to Mr. Trump.

But even with Mr. Bannon off the field, the party is riven by factions.