There's no cap on how many daily games you can play at the same time
Should Chess.com limit the number of simultaneous Daily Games for players

No cap but from reading previous posts seems it effects game play level. I get worn out playing 1 game 😜

I just played a daily game against a relatively new player that is obviously quite strong due to 1700 Blitz rating. But then I saw he played 150 daily games simultaneously that he mostly started around the same time, which I found optimistic. And sure enough, after move 10, he lost on time. I checked, and he seems to have lost all his other 24 hour games as well (around 50 at least). This is of course highly annoying for all those players.
In my view, you should not be able to start as many simultaneous daily games until you have shown that you can handle it. So maybe start with a maximum of 10 or 20 simultaneous games and only if you complete those games should you be able to play more simultaneous games, i.e. maybe 10 more.
I asked a moderator, and he answered that he doesn’t think there is a limit.