I have not pinched back milkweed on purpose to try for more bloom, but often stems and flower stalks get cut or broken, amounting to the same effect. I will get lots of new growth, but never new bloom. The species I have seem to be programmed for one flush of bloom. I get the most re-growth on the swamp milkweed (A. incarnata). I do not have 'red milkweed' (A. lanceolata) as it is not hardy here.
I barely get pods formed on my tropical MW (A. curassavica) before frost, and usually have to bring in the plants (under lights) for the pods to mature. My tropical is peaking in bloom now... I hope the pollinators get busy on it! I now go days without seeing a monarch, although I hear reports of lots of migrating monarchs along the shore of Lake Ontario which is about 60 miles south of here. Our hummingbirds now seem to have left the garden as well
I have lots of pods on the swamp milkweed. The flowering plant to the right in the photo is Joe-Pye Weed. Both in my garden and in the wild around here, the various Joe-Pye Weeds take over as an important nectar source for the butterflies. I must say though, that the real favourite nectar plant this year (for the butterflies) has been the Mexican Sunflower (grown as an annual here).