I would strip all of those shoots flowers etc off, if you are not saving them they will just be competition. If you want to keep the base variety just keep a few buds in the appropriate spots. A couple shoots left lower down probably won’t be a problem but trees feed the healthy buds more than the half-there ones so your grafts have a chance of starving out if there is too much competition.
Here is one of my peaches from a week ago just barely budding out now:
I know this is a good one partly based on experience - its green and its coming right in the middle where the leaf bud is on a peach. Right now maybe 1/4th of my peaches are showing this kind of thing, a few are a bit further along than this one.
Note I am not showing this tree but this scaffold is competely stripped. The other scaffold I trimmed to about a foot of budding shoot total, I will probably graft that part over tomorrow and remove every single bud from it. It could be the graft would tolerate a bit more competition but I’ve lost too many things from competition. You can also have the problem with multiple grafts at the same time that one graft will out-compete the other. So in some cases your plan to add five varieties at once will end up being only three. For apples and plums this is usually not a problem but it can be a problem for peaches and persimmons amongst others.