Is it possible to add new rats to a cage with existing rats?

Yes, especially if the rats are both still younger than 4 months or so.

When rats are full grown, they may feel they need to defend their territory from newcomers.  This is true for both male and female rats.  In the case of male rats, if you can get the alpha rat to accept the newcomer, the others will follow his lead.  Females have less of a strict hierarchy, which means that each rat will make her own independent judgement: some females can be very nasty with younger rats for some reason, so some suggest to wait until young females are 8 weeks old before introducing them into a colony.

The easiest way to introduce new rats is to let them play together, supervised, in a neutral place.  You can also try putting some vanilla extract on the new rat’s belly, chest and rump, so they don’t smell more like a milkshake than a strange rat.  Keep a water sprayer handy to break up fights.  If it doesn’t work out at first, try again later.  Don’t force things, and be prepared for the possibility that you may need to keep some rats separate from others.

Good luck!