My S attempted to meet two teachers at one school. He sent a single email to both of them, explained that both of them had been recommended to him, and he would be making a trip that direction and would very much like the opportunity to meet them and take a sample lesson.
As it turned out, he was able to actually get a lesson with only one of them. The other was going to be on the opposite coast during our time frame. But they both responded, and neither treated it like it was anything unusual. I think as long as you are open about it, no one cares. [That's the nice thing about horn players - they're all so nice
!]
At another school, he arranged a lesson with one teacher, who then took him around to meet one of the other teachers.