If you have to ask, the answer is probably no.
"Should" is subjective. The use of the words "gave in" worry me the most. It will change your relationship and the maturity of everyone involved is what will set the tone and the consequences for the choice. You have to set boundaries.
My partner and I talk about threesomes all of the time and I think right now we aren't willing to pull the trigger because of the law of unintended consequences. We just don't know for sure what will happen. We have had threesomes before and they were disasterous but it had everything to do with the third person we chose and not necessarily our relationship itself. If that makes sense.
I suggest reading The Ethical Slut and really talking about it thoroughly with your partner. Set boundaries and code words that let each other know you are feeling uncomfortable with something going on and both people should have the freedom to say "STOP" without fear of an argument or hurt feelings.