Does he have a lovely he can hold onto? Maybe something you can power up with mummy love and tell him when he wakes at night he should hold it and cuddle it and go back to sleep? You could do a little role play during the day, get into his bed and say you are pretending to be him, show him how you wake, find the lovey, snuggle into it and get all the mummy love and turn over and go back to sleep. Then get him to have a practice. I've done this with a few different things with my DS and it worked pretty well for him to know how to respond.
You could also explain to him how everyone needs their sleep so that they have enough energy to play properly the next day. Explain how he is waking his sister which means mummy has to also go to her which then means less sleep for mummy and less energy to play well. Let him know you love playing with him and want it to be good fun so lets all sleep quietly all night.
You could verbally reassure from outside the room to tell him to go back to sleep without going into his room.
I had a phase with mine when he was calling out for pretty much no reason, I ended up calling back that "I'm right here everything is fine go to sleep" then " go to sleep" and in my less patient moments in the middle of the night I called "It's not fair, I need sleep too" and if he shouted again I called back "be quiet, go to sleep". Whilst I sometimes felt less than great about not going in to him I also knew that he had received the verbal reassurance, he knew I was close, he was not abandoned, he was safe, that I would go to him if there was a real problem but that actually in the middle of the night it was not acceptable to keep calling out.
Children who are not responded to might fear they are not safe or there is no one watching out for them, children who are responded to even if it is "go to sleep" are reassured that mummy is still around. Obviously if they are crying and distressed it is different, but this waking and just habitually calling for a little cuddle is different, they are not in pain or ill or in danger and I think a verbal response instructing them what to do (be quiet, go to sleep) is an acceptable one.
If the twins are still napping you might find that this twin needs less nap, capping his nap may help with nights. Some LOs have dropped their nap by this age so it wouldn't be unheard of although totally cutting the nap out would likely cause a period of disturbed sleep whilst a new suitable routine was established.
Otherwise...keep telling yourself it won't go on for ever. It must feel like it now he is 3yo, but he really is likely to stop this eventually.
hugs, it really is exhausting to have your sleep broken and perhaps more frustrating to know that it doesn't really need to be as he is basically fine.