No, you wouldn't want to add more, as stirring would disrupt the coagulating process. I use the so-called "flocculation" method, where after adding rennet you start watching and timing until the milk begins to gel (either the spinning-bowl/lid method or dipping-knife method etc). Then once that happens you can figure out how much longer to allow the milk to set. So, for instance, whereby for a recipe the ideal flocculation point would have been at 12 minutes, it may have taken me 18 minutes once my rennet was getting older. So I just allowed the total time before cutting to be longer, and when making cheese the next time, I increased my rennet until the timing seemed more on the mark. Conversely, when I first started making cheese with the new rennet, I was getting flocculation at, say, 8 minutes, so it was rather quick. I think you'll wind up with fairly the same strength of curd either way, if you are careful to use the timing method - but there would be differences, such as a longer-than-called-for coagulating time leading also to more acid production in that interval.
