It's OK to start a new trial during another. I've been starting a new trial almost every week over the past couple of months. The key is to make sure you balance them. If you're doing a trial that fairly difficult than do something that's a little easier the next week.
I see that you're interested in doing a "Talking to Strangers" trial.
I actually started that two weeks ago:
Life Experiment #7: Talk To Strangers Everyday For 30 Days | The Life Experimenter
My biggest piece of advice for that is to join groups on Meetup.com that interest you. You'll be forced to introduce yourself to every meeting that you go to and you get to spend time doing things you enjoy.
Good luck with you trials.
-Allen Rinehart