Hi Piper,
My son would have a longer stretch of sleep at the beginning of the night, of varying lengths, but from that first wake up it was every 3 hrs, sometimes even less. if you`re giving him that much formula during his dreamfeed, you wouldn`t think he`d be up 3 hrs later again - maybe it`s the habit. I used to try to dreamfeed my baby but then he started to wake for it and expect it, still waking up 3 hours later.
So, yes, I was up every few hours at night. I`m still up a lot, sometimes for milk, sometimes just because he`s woken up and can`t get himself back to sleep(he got used to the breast but now sometimes doesn`t even want it yet cannot sleep without it. angry baby at 3am

).
I introduced solids at a week before his 5th month because he turned into a serious milk monster and stopped gaining weight. I was feeding him round the clock nearly every hour - I couldn`t keep up, nor did I want to. Nothing happened overnight, but he does sleep better than before. Then again, we are really hit or miss on the sleep thing. Sometimes he still wakes up a lot (not always for milk but at least once a night), sometimes he doesn`t. He`s on 3 full meals a day (at nearly 8 months) and it`s helped but it`s more of a habit now. Or it`s teething. Or separation anxiety. Or learning a new skill. It`s always something, it seems

I kept counting the occasionally increasing stretches of sleep -4 hrs, 4.5, 5,6,7 -yes even a 7!
But, you know what, it doesn`t matter. You are probably so programmed to waking up so frequently that even if your baby doesn`t wake up, you will, and wonder what`s happening and check his breathing, etc. And after that nearly full night`s sleep I once had (about 2 weeks ago), I felt no better in the morning.