Yikes, I did three this month and am happy to have a few weeks until being on call again.
I had one client go a week over from Feb and two clients due on 3/28 go at 37 and 38 weeks. I almost had a third client, but she lost her baby :( But I think that might have ended up being too much for me.
Next month I will have 2-3 again, depending on when they all go. Only one is actually due in April, the other two are due on May 11. Then I will be done until September, ideally, but will not turn any births down if I am contacted in between.
So after all that, my personal limit is 2-3 per month... probably closer to 2 with a random 3 in there occasionally.