Way to ctrl+select points of only one shape?

[Koopa1018]

I am attempting to split my H into three shapes: two stems, one crossbar. I've pasted the full-H shape three times, and removed from each shape the points which were not needed. However, in doing this, I ran into a problem: when I hold CTRL to select multiple points, all shapes' points become highlighted. This makes it problematic to ensure I'm deleting the left ascender from the crossbar shape rather than from the left ascender shape. I ended up having to move all three shapes apart from each other and then manually reposition them once I was done.