You can mix and match airlines on almost any ticket, as long as the airlines have interline ticketing agreements with each other. In terms of pricing, it depends on the fare rules. In some cases, the total fare will be the sum of fares on each airline. In other cases, one airline could publish a fare, which allows travel on another airline (excluding codeshares.) This applies mainly for international fares.

In terms of baggage, call the airlines directly and see if they have an interline baggage agreement. Most do.

Welcome to FT.