The only real way is to overexpose. The lost speed is lost speed, and increased fog is increased fog. If you push process, you increase the fog even more. If the fog is a problem, you can PULL process or use an antifoggant, but then you will be decreasing the speed even more.
So, I think for overaged film shot at the original ISO, the normal development is near the best you can get.
If you can overexpose it (which you really should always do with old film), then again, normal development may again be near the best, but now there is a possibility to fiddle with antifoggants to get snappier shadows with less fog.
Slide films typically have a severe fog problem when old, ruining the blacks. In that case, overexposure and PULL processing helps a lot. Antifoggant would probably help even more, but pull processing is easier to get. But with negs, you can just print through the fog.
With old film, bracketing the exposures is important. For old negative, you could make two exposures, one +1 and the other +2.