First check for clogs. But if you need another one, put it on the other side. Best if you can get half the gutter sloped that way. Also, use 3" x 4" openings, if you can. If you have smaller, it's a good idea to replace them, as well as use 3x4 downspouts.

Is putting one in the middle of run (as opposed to the corners) an unusual setup?

In my case the sloped area is a driveway that slopes towards a garage. No grass/soil to take the runoff if I were to put one or two at those corners.

You'll see numerous downspouts on a long run, such as an apartment complex. However, the gutter is sloped so the downspouts get equal amount of water, roof area also comes into play. Can't remember and am too lazy to look up, how much fall you need for each foot of gutter.

On a residential setup, it would look odd to me to have one in the middle and one on the end. One on each end would look more symmetrical. In which case the high point of the gutter would be in the middle, with fall to each end. So you would have to rehang the gutter.

Just my opinion, messing around with gutters/downspouts is too darn dangerous and time consuming for the average person. Gutter runners can tear down and run seamless gutters in a matter of hours. They can provide the correct fall, hidden hangers (additional charge vs spike & ferrule), and give you a professional job at a reasonable costs.

Is it unusual to only have 2 downspouts (both on same side) for an entire house?

Depends on the size of the house. Mine only has 2 downspouts at the front of the house and it works fine.

I only have 2 downspouts. They both come down on north side of the structure, but 1 gutter is on the west side, the other on the east side. Typical gable roof style.