shop around

verb3

1. •
   To actively search and compare options before making a selection or choice of vendor.

   • He's gone to shop around for a new car.
2. •
   To actively make a search for an alternative choice of something one has, owns, or wants, without it necessarily involving buying or selling anything.

   • She's shopping around for a new boyfriend.
3. •
   To put something out on offer to multiple parties in the hope one will choose it.

   • He's shopping around his book to several studios. He hopes to get a movie deal.