I'm going through it too but I'm not planning on sleep training yet. Every second I'm on my phone at the moment I'm desperately googling 4 month sleep regression and from what I've read training isn't recommended during regressions. Most articles seem to recommend sticking to a regimented bedtime routine and riding it out.
My baby was crap at napping but great at night until probably 14 weeks. He would go down between 7:30 and 8 easily (FF to sleep) after a bath, then wake anywhere between 12 and 1am and again around 4am, up for the day at 6am. I could deal with that. Even felt refreshed after that first 4/5 hour stretch.
He's just gone 16 weeks old this last Friday and for the past fortnight his night sleep is getting increasingly bad. It started with 1 extra wake around 10:30/11pm. Last night he went down at 7:50pm, woke up at 8:30, 9:30, 10:40, midnight, 1:30, 3, 3:30 at which point I brought him into bed with me because I'd had enough. I would say co-sleep to get through it, but mine doesn't sleep well on the bed with me either. I have to hold/cuddle him lying down to sleep and even then it is a very light sleep and he's stirring every 10 minutes. I can just about get him through to 6am with the feed about 4:30. I do hate cosleeping though and worry about the risks but after two weeks of about 3 hours of broken sleep a night I'm just doing what I have to in order to stay sane and awake during the day.
Not feeding every time he wakes up obviously, but feeding around 11, 2 and 4 and he is hungry and usually has 5oz a time.
Probably creating a shed load of bad habits I'll have to break at some point but honestly I'm too knackered to even care at this point. Wouldn't mind if day naps were good and I could grab an hour here or there but he only contact naps for 30 minutes at a time.
So no advice but big hand hold, massive cup of coffee, and solidarity, this regression is absolute dog shit. I've read threads of people saying their baby was over it in 1 week, and I know one mother IRL who has a 9 month old and her sleep never recovered after the 4 month regression! Let's pray we are not part of that crap club. Back to sleep training, I would consider training if my baby isn't over it within 1-2 months, so if sleep stays this way and doesn't improve by 6 months, I will be researching sleep training for then. I'm also considering hungry baby milk but we have health clinic on Wednesday for a weigh in so I'm planning to ask about this then as heard mixed things, will try and report back!