There's no limit to the number of apps you can submit.
I've found that it's better to have your clients sign up for their own developer accounts and to add you as an administrator of the account. That allows you to create certificates, etc., but the app shows up under their name.
It also means that they can easily do whatever they want with it down the road. You can't transfer an app from one company to another, but you can effectively hand over your entire developer account, allowing them to sell the app to someone else if desired. If you keep it under your company/name then it'll always be there.
Lastly, it allows them to view their own iTunes Connect sales/download information without having access to your other clients. Without it you'll have to provide portions of the reports yourself, or summarize for them, or whatever. Probably seems reasonable now but two years from now, say, there's a good chance you'd rather be out of the loop, especially if the app isn't selling well but they still need to know.