Yes. One way to multi-game is to click on the "Play" option and from there choose Live Chess (real-time games) or Daily Chess (postal chess). You can also offer a challenge or accept one created by another player. You can configure the time settings in all of these except for another player's challenge that you accepted. That's how I do it using the mobile app. The website might be a bit different but not that much.
Multiple games at once?

I think that's still a premium only feature. Too many players were abusing it by starting another game when they were losing and just letting the clock run out.

I have a premium membership (diamond) but I still can't figure out how to play multiple friends at once...
On the website, there is a live chess setting which enables simultaneous games. It's not possible with the apps.

I started two new daily games and was waiting for a match. While waiting I started a 30 min game. While playing the 30 min I made a move in the daily game and could not get back in to the 30 min and lost that game on time. How do I get back into a game. It did not show up on my home page, it was like it didn't exist until it showed up when I lost on time

ok...
in daily multiple games is a normal thing
multiple live games looks to not be a thing
and daily + live is ok (cuz otherwise all of your live playing would be cut because of playing daily) but playing a move in the daily when in the live and there are two cases
if the daily is in another tab then well you may just be removed with doing this continually coz it looks sus to go to another tab often (engine)
and in the same tab, well obviously it wont let you come back, you would already be flagged as disconnected
but maybe you can do a daily in a phone while doing live on a computer (though why you wont just wait for the live to finish so then you can think about the daily confuses me)
Does chess.com have an option to play multiple games at once? And if so what does it look like?