Could the James Corden Carpool Karaoke Empire be expanding?

According to this Trade Mark application filed with the European Trade Mark Office, yes.

Carpool Karaoke

Here’s one of my favourites, while we’re at it:

Just FYI James Corden himself doesn’t have his name registered as a Trade Mark (which he should), but other things associated with him, for example Gavin and Stacy are Trade Marked (by the production company that produced it, Steve Coogan’s Baby Cow Productions Limited)

Gavin And Stacey