Is it possible to setup your own proxy server network?

I've tried out a few different proxy services and the best I've found is proxymesh.com, but sometimes websites I try to scrape don't return a response when I make a request through the proxy (while they do when I make the requests without the proxy) which indicates other people are scraping those sites and the sites are blocking the IP.

This is going to be a problem with any proxy service I use, so I'm just wondering what goes into creating your own proxy network? Is it possible? The main question I have is how you would get multiple IPs and rotate them once or twice a day.

You need to either rent blocks of ips from an isp or to negotiate with a provider on a monthly fee (usually 1 ip is 1$ / month ). To have a rotating ip you need HAproxy (act as a load balancer between multiple ones).
Best of luck in your journey