I've never really "shopped around" for a t unless the one I was seeing at the time was obviously a poor fit. That's only happened once or twice out of 19 years in therapy (with about as many therapists as i was seeing students a lot of the time). Over the years, I think I managed to figure out what worked for me, and what didn't. I don't think I would have known any better the first dozen t's or so...

Conversely, my wife has had some t's who seemed to do little to nothing for her. They neither offered much support/understanding, nor helped her with any of her presenting issues. She stuck with them in holes of gaining something, but after several sessions would simply stop rescheduling appointments. I'm not sure how much of that is her lack of investment in therapy (because she expects therapy to be something it's not?) Any how much is simply the wrong fit...

If you think it might help to interview other t's in hopes of finding a better fit, I don't see why you shouldn't. It may be worth taking to current t about your questions though. Sometimes a t's response to normal curiosity and questioning can give you very telling answers. I've only had one t get defensive and insulted by my questioning, and they turned out to be a really bad fit for me....