How much pruning should I do to help the shoots that are growing from my recent grafts?

At this point I have only removed shoots that are sprouting near the grafted bud shoot (within a foot or so).

Should I remove all shoots originating from the same limb (like those that are sprouting from the base of the limb 2-3 feet away)?

Should I remove other adjacent limbs that are growing out over the grafted shoots?

if the new sprouts are vigorous and are growing in the direction of opening in the canopy that would make the tree more balanced, then graft you slower growing cultivar over them, or graft additional varieties.

You can easily end up with a 1,000-n-1 and yet perfectly balanced tree given the time and space,

Instead of pruning, I just do grafting for balance, it is the same effort, actually more pleasure for me. But to each their own way of tree maintenance.

So you don't do any pruning to help the new shoots grow? Do you even leave the shoots that start near the grafted bud shoots?

If the grafted plant is vigorous, it doesn't need any help. In most cases, I want to slow them down instead of speeding them up. So I let them fruit the first year grafted.