One of the best ways to search for fish when there isn't a hatch or to cover all of the stages of a hatch is to use multiple flies at once. Most seasoned fly anglers have used a big dry fly with a dropper nymph but several other variations on the multiple fly rig also work very well.
For fishing deep runs or pools where fish may feed at several different levels one good set up is to use 2 or 3 nymphs, where legal of course, to cover these different depths. This can best be accomplished by using a heavy nymph like a tungsten wired prince, tung teaser, or other tungsten bead nymph in size 10, 12, or 14 tied onto the point of the leader. Then tie one or two unweighted or small beaded nymphs like ghost nymphs, hares ears, bird's nests, or other appropriate flies for your river off of droppers spaced anywhere from 12 to 24 inches apart going up the leader. The heavy fly should drift along the bottom while the lighter fly or flies will cover the other depths. Fish this either under a strike indicator or Polish style.
Another set up that anglers overlook is the multiple dry fly rig. This works in several different scenarios. One good way to do this is to use a large bright dry fly for visibility and a hatch matching dry fly 12 to 20 inches behind it. Also, it sometimes pays to use 2 or even 3 hatch matching dries to figure out what exactly the fish want. Then you can switch to just a single fly of the variety that seems to work best or, even though it sounds a little funny, put on 2 or 3 of the same dry fly in slightly different sizes or hues to further refine your offering. Once you have it dialed in throw 2 or even 3, where legal, of the exact same fly. Create your own mini-hatch.
These are just a couple of the ways you can rig multiple flies. Think about what the fish are doing and you can probably come up with several other multiple fly rigs that are appropriate for your situation. Good luck and see you on the water.