I don't think there's really a set time frame to use as a standard, but one could ask themselves, "How much energy do I have to put into starting a new relationship now?"
When I first chose to pursue polyamory as an approach to relationships, I was newly separated. So, I thought that, since I was starting at "zero partners" and my goal was multiple partners, I should begin several relationships at the same time. I started dating a few people and I still think it's possible to start a few relationships at once. But in actuality, I had some issues in my life I didn't want to face, really, so having multiple romances was a much more exciting thing to focus on!
Things started fizzling out with my guys and all of a sudden I was at zero again. Then I met someone and dated others after I started to see him, but those other urgent issues in my life began demanding my attention, and I had to deal with it all, finally. Eventually, I felt much more prepared to pursue other relationships. And things seemed to move in that direction without too much effort.
So I believe that if it's the right time, you'll know it. I don't think there is a formula. I think it's more a question of how much can fit into one's life. Things will start happening and falling into place for an additional relationship to work itself into one's life exactly when it's time for things to start happening and falling into place.
So how do you deal with it?
Hmmm, what is the "it" in your sentence,"how do you deal with it?" Do you mean "how do you deal with starting new relationships?", "how do you deal with your partners starting new relationships?", or "how do you deal with your partners' reactions to your starting new relationships?"