There is some good stuff to read if you Google 'pruning philadelphus' Muddyshoes. If I recall it is rather detailed and difficult to repeat here. You can do it but please study it beforehand.

I think the general rule for philadelphus is , after flowering has finished, to prune everything back to about a third of its present length and then after that cut down to ground level about one in three of the branches.

So for you it sounds as if its the big thick ones that will be cut right down . And thats what I do with mine, I take out the oldest thickest branches. Perhaps I am doing something right because this year it was just covered in flowers.

I would take out about a third of the very old branches, right to 6-12 inches from the base. This will encourage new growth that will flower next year. Do this pruning every year (with the oldest stems) and the plant stays young and vigourous.