I'm an English teacher on italki, and quite a few of my students have classes with other teachers. I don't mind, and I have noticed it gives my students more confidence. 

There are however some protocols that I think it's advisable to follow; never talk about the other teachers or their teaching style with another teacher, and if a teacher asks, then you should probably be wary of them. Also, try to leave a few hours between teachers so that the teaching style of one teacher doesn't immediately affect the class you have with another teacher. 

Other than that, good luck!

Sure! It's actually necessary. Learning a language is not like learning mathematics (well, learning Russian language is pretty much like studyiing mathematics, but...anyway)... it gives you the ability to have more practice, learn " the same thing " in a different way, get to know different views, accents and experience. Especially if you're learning more in a conversational way. I always suggest my students, for example, to try other tutors, especially from Portugal, so they can compare and see if they'd have problems with a very different variant of the language. It's healthy to do it! :)

I'm learning Russian, for instance. And I have selected some tutors. I have tutors that are AWESOME to teach Grammar in a fun and interactive way, so I always go back to this one so I can improve my grammar. I have others that are AMAZING to get you more confident and talk, it's perfect to express myself better and put into practice the grammar that I learnt from the other one. I have another one that helps me increase vocabulary and with reading sessions which I find important when I'm learning Russian, and I try other tutors for conversation, so I find it actually great and I suggest everybody to do so! 

I have been studying Spanish for 4 years.  I've had private tutors and group sessions.  One thing I like about group sessions, is that you can learn from others, which I find to be helpful.  Also, my experience has been that sometimes, if I've been through a particularly tough day of language learning, it's nice to have others there who have a chance to speak which takes some of the pressure off you, which is nice - for those moments when you just need a mental break!  Of course, the benefit of having a private tutor is that you get the chance to focus on your particular weaknesses and you get the opportunity to drive the agenda.  

I'm new to italki, but my experience has been that it's also beneficial to have different teachers - from different countries if possible, so that you can get used to hearing different expressions, idioms, accents, etc.  

When I first started studying Spanish I was in group classes, but as I've advanced in my studies, I'm finding that I benefit more from individual classes.

That's been my experience!

Best of luck to you!