While targeting trout, anglers tend to fish multiple flies. Fishing 2 or even 3 nymphs under an indicator has been practiced for years. Fish one large attractor pattern followed by a smaller more specific imitation. This covers multiple food sources and depths in the water column. Next in the world of tandem rigs came the dry dropper approach. This allowed us to cover surface and subsurface feeding, all in one rig. The more popular tandem rigs got, the more people started to play around with them. Soon double dry fly rigs were a thing. Cover two different insects or sizes of bugs on the same drift. Some of the time I fish multiple dries as having a large #12 on there is the only way I can find my tiny #22 Parachute Adams in the water. Fishing multiple flies is typically better than one (again just focusing on trout fishing here). Another type of tandem rig that you should consider, fishing two different streamers at once.
This may sound excessive or even a little dangerous to cast (think chuck and duck) but I am here to tell you that fishing multiple streamers is a great way to increase your number of eats! I will often use a heavier rod when doing this to help in turning the heavy, multiple fly rig over. A 7 or even an 8 weight is not overkill when fishing double streamer rigs. Then I typically mix and match flies, a little salt and pepper if you will. By this I mean one white fly and one dark fly. Or one flashy fly and one more neutral color. One big fly paired with one small. It is a great way to fish two very different fly sizes, colors, and profiles until you figure out what the fish are keying in on. I attach the second streamer just like I would tying any dropper by simply adding the line off the bend of the first hook.
Often times, especially on clear sunny days, I find I get lots of fish following my streamers but not eating. A second fly on there is a great trick to seal the deal. The fish may turn off your first fly, but a second meal coming behind is often hard to refuse. If I am fishing two different sized streamers, I will put the smaller fly first with a larger articulated streamer after. This can also give the appearance of a medium sized baitfish chasing a smaller bait fish. Now that predator brown trout has two different meal options to choose between! I prefer the articulated fly to be the second one here because I do not like anything tied off the back hook of the articulated streamer. I always feel this could affect the movement of the pattern. To avoid this, I fish a single hooked streamer first (sparkle minnow is a personal favorite of mine) then hang the articulated pattern off the back. Another weird but for some reason effective approach, hang a large stonefly or egg pattern behind your streamer. I know stripping a streamer in is not how a stonefly naturally moves in the water but this is just something I cannot explain. If fish are being especially streamer shy, a nymph tied behind the streamer can be a day savor. Remember there are no rules on how flies should be fished (minus of course snagging or number of hooks on a single rig regulations which vary by state), so mix it up out there! You never know what might lead to some success and ideas on other rigs.
Other Rigging Suggestions: