J.S.
My son (he'll be 4mo on Monday) has been sleeping through the night since he was 6wks. He was also taking little catnaps through the day. I asked the doctor and he said it was fine as long as he is getting the long stretch at night. Some days he will only sleep 8hrs total, then some days its 16hrs total. He may be going through a growth spurt that's making his sleep schedule go haywire. I personally think 11wks is a little young to be letting him cry it out, but don't judge if it works for you. From what I've read, babies don't learn to trust until 3mo, so he's in there crying because he's lonely. It may help to take the extra time to rock him to sleep. I know my son is not completely asleep until I can lift his arm and it falls right back down. Do you offer a pacifier? He may need something soothing like that. I know my son can go to sleep without his pacifier, but he sleeps better if he has it. He also likes having his "Tuggy." It's one of those tiny blankets that has the teddy bear head on it. If you are formula feeding it may be time to up the ounces you are offering. He may not be completely full, so he's really hungry when you're thinking he's still tired. 2-2.5mo was when I went from 20oz to 24oz a day.
Hopefully some of this will help you. Good luck and sweet dreams!