There are a number of outfits that make multichannel amps, however 16 channels (8 zones x 2 speakers each zone) is on the high side. 12 channels is about the most I've seen commonly available.
I think Crown and QSC both make multichannel amps, but not sure about how many channels.
Searching the Internet for multichannel amps should get you quite a number of results.
Also, if you are going to regularly use the gain controls as volume controls, be advised that often when dealing with a high count of channels in one chassis, the controls probably won't be front-mounted knobs. More likely, small trim pots that you need to adjust on the back panel, possibly with a small screwdriver.
If mono sound is suitable (sort of assumed stereo at first), it
could reduce your number of amp channels or volume controls by half, and may even be preferable to stereo depending on what your needs are.
Here is an amp that would handle your 16 speakers in 8 zones of mono pairs just fine with no worries of overheating, etc.
Some info about the speakers, the install, and the use of it all would be helpful for better advice.