Raising canopy of tree

Got a lovely wild holly which is now nearly twenty years old.
I would like to raise the canopy on it to stop young saplings growing and competing with the holly.
It has finished flowering and new growth is starting to appear, could I take off a few lower limbs to see if I can then get at the growths underneath?
I only wish to raise it enough to get at those seedlings and growth which will make it look a bit of a mess.

 

You're supposed to prune them in mid winter. I've only ever pruned my holles a week or 2 before Xmas when I can give the prunings away.

 

If the canopy is dragging, then we used to raise it after flowering. This would encourage new growth at the top.