Introducing adult cats, need advice!

by Amy
(USA)

I have two adult cats, 7 years old, one male (Romeo) one female (Tigerlily) raised from kittens.

I had to take another two males (Leo and Tigger) from a bad situation. They were from my previous relationship, so they both know me very well. Both of them are close with each other and get along. Both about 5-6 years old.

Romeo is friendly and previously showed interest in another adult cat that we had briefly years ago. However, he can be quite shy with strangers.

Tigerlily isn't very social with anyone and tolerates Romeo even from kittens, but Romeo is high energy. She likes to sleep and only wants to be petted when she's after something.

Got Leo and Tigger 2 days ago and they settled in really quickly, no hiding etc. I've kept them in my room separately from the rest of the house for now.

I have read some things online about introducing adult cats but this is introducing two cats to another two. I have hopes for all the males getting along as they all have roughly the same personality and are curious and show no signs of aggression.

I'm worried about Tigerlily as she smelled the room the newcomers were in and was hissing and growling, then at me and even at Romeo. She seemed stressed. They've seen each other but haven't come into contact.

Any advice? I know Tigerlily is who she is and will never be best friends with anybody but I at least want her to tolerate them like she does Romeo.