Multiport cable TV distribution amps for more than 8 TVs?

Title pretty much says it all. We have about 20 TVs at our business and the signal quality isn't the greatest. It isn't really that bad on TVs in people's offices, but on some of the big screens we have you can really tell the signal's been split a few times.

The cable line comes in from the cable co to a single port amp, which then goes through a chain of 4 port splitters. I.E. the line coming off the amp goes to the input of the first splitter, ports 1, 2, and 3 on the splitter go to TVs and port 4 on the splitter goes to the input of splitter #2, and so on.

I'm trying to figure out the best way to boost the signal. Does somebody make a 20 port amp? Or would I need three 8 port amps? Can I daisy chain amps or is that bad?