I once tried to remove a small male holly tree by clipping off every single branch and leaf. I was left with a single upright... bare-naked, as it were. The trunk was slightly too big for my pruning lops, so I made arrangements with Mr.P to cut it off at ground level. He never got round to it and now that critter is bushier and more vigorous than ever. I just checked... about fifteen month ago it was a single stick 5 feet high. It is just over 5 feet high now.... and about five feet across. There are multiple stems (where'd they come from?) and a passle of broad leafy branches.
I remember when it first started its regrowth, the holly leaves were so tiny and cute that I was entranced. Unfortunately they've grown back to full-size. My experience is that Holly is an extremely strong plant that responds very well to pruning. You may, however, want to wait to prune until late fall... just so you can use the leaves for Yule decorations.
(I guess I should have known better. I later found out that cutting down holly and other thorny trees is
considered bad luck by the Celts and other inhabitants of the British Isles... these trees are the homes of fairies and other wood sprites.
)