Dogs not getting along

TL;DR. Newly adopted male dog is starting to push back against my female dog, who has been guarding me from him for two weeks. I’m worried about it getting out of hand.

I have had my female chi-peke for about 6 years, she’s about 9 years old. I also have a 4.5 year old Chi mix male that I adopted 3.5 years ago. The female has always been possessive of me and often runs the male off if she is with me first. If he is already with me, she’s usually fine. I run interference as much as possible as he is timid and nervous and I don’t want her to be mean to him or monopolize my attention.

Two weeks ago I adopted a 3 year old male poodle mix. He has attached himself to me, follows me from room to room, and always wants to be near me. I have stopped the female from bullying him, and let him be with me, while still giving her a lot of attention. He is very sweet and he hasn’t stood his ground with her until today.

He is sleeping next to me on the couch, and she hopped up next to him to be near me. I heard a low growl, and thought it could be him, but since he had never done that before, I assumed it was the female. She tried jumping up again and he snapped at her. Granted, he was already there and sleeping, and I understand why he would not want her jumping up near him, but she didn’t make contact.

I’m concerned that these behaviors may escalate, and I’ll have a scuffle on my hands. I want him to be able to spend time with me, but I also don’t want her to be pushed out. It wouldn’t be fair to her.

What should I do? I have a fair amount of experience with dogs, but this is a new one for me. If necessary I will get in a professional trainer to work through this. I’m wondering if getting a third dog was a mistake. Any advice appreciated.