Here in the UK many anglers use more than one fly on both stillwaters and rivers The traditional rod for river wet fly fishing trends to a bit on the softer side and longish. The idea is for slower casting with bigger loops so that you don't tangle up your flies. Also a softer drop onto the water.
With loch-style fishing, the casting is short line but with a longish rod, only a few years ago a loch rod was 11.5ft quite commonly. Most go for about 10ft now.
As I said the soft rod is the safest way to cast a multiple fly set-up. The most common rod now-a-days on the river is a 9ft.
I recently decided to go back to the longer rod for soft hackles etc for river fishing. I bought a 10ft wt 4, which I have yet to try out. Only a few more weeks.
The above statement is only my opinion, no doubt someone will say they can use a 6.5ft rod to cast 16 flies nae bother.