L.D.
You mention that he has a speech therapist. Is this through the school? If so, you may want to consider seeing if your insurance will cover the cost of having your son receive additional therapy through a private speech therapist. My experience has been that a school speech therapist only does so much and it's usually not enough. What worked best for my son was having the school ST and private ST collaborate so that they were generally working on similar goals at the same time.
Doing the ST homework that they give you is crucial. So was making sure that our son was in a structured preschool setting and had lots of exposure to typical peers. Making sure that he has the opportunity to talk instead of having people talk for him is crucial. Holding back on giving you want he wants until he says some semblance of "More milk please," (or some similar 3-word sentence) would also help. And giving it some time is also important. He's languaged delayed but he's still only 3-years old and quite young still. Our son was/is language delayed also and we did what we could as soon as we found out, just like you. We started noticing a large gain in language when he was in kindergarten and it's just been gaining momentum ever since. I guess that was the perfect right time for him to really start talking. I'm sure, as long as you are being proactive, you'll see similar results very soon.
Wishing you and your son all the best this holiday season.