As advised, some will, but it is always more economical, not to say simpler, to get your frames from the same optician as you are getting your lenses.
The only way it's viable is if your lenses are sufficiently inexpensive, that the cost of fitting and frames separately is still less expensive than buying the two from the same optician.
I am lucky as near me there is a firm which makes spectacles for the trade but will also sell to the public. They don't do eye tests but if you take your prescription to them they are a fraction of the cost. When I broke my specs (lenses intact) I went to them and they fitted the lenses into an identical pair of frames for £40, for which I had paid the optician £200.
They dont like to do it because they cant guarantee the frame. However, if you insist the going rate is £50. Priced that way as they rather you to buy a cheap set £25/40ish
Just a caveat - if you're going for varifocal lenses I'd buy them with the frames from the optician that tests your eyes. Varifocal lenses need to be placed very accurately in the frames and I've had more than one occasion when the lenses have had to be remade to get the positioning correct; it even involved a retest on one occasion. If you get things done separately you might get into a situation where each blames the other for the specs not being right.
In addition to the last remark....you may find that the frames you choose are not suitable for your prescription eg lenses too thick (or thin) at the edge to fit your chosen frame properly.
they are cheaper as they are not made of glass, but i have had many pairs from here and they are fine - good thing is, if you break a pair you can just get another, and also have a few pairs
NB - i think the frames MUST have small screws in each eye though, or they cant be done - but double check with them in case they can do something