When looking at this it's tempting to want a complete squad with absolutely no weaknesses, but I don't think it's actually necessary to "compete". It's just when you have an incomplete squad you're likely to find yourself falling short rather than going all the way, like Arsenal have found. Even City's squad has issues, they have basically 1 full back in their squad at the minute in Walker, I'm sure they'd love a pacy winger to give them something different etc.
To compete for the league you really need to aim for 90 points, and to actually win it you have to hope City have an off-season where they dip below 90. Basically we need to find another ~20 points from somewhere next season.
In terms of first 11, I think we'd need minimum a goalkeeper, midfielder, and striker. If you got 3 elite signings in the first 11 then it's not that far-fetched that can be worth an extra 15, 20 points over a season which would put us in a title challenge next season. I think a top class striker in this team this season could have been worth 10 points alone given we've had absolutely nothing up there all season.
However that still leaves holes in the team, right back needs an upgrade, another midfielder to replace Fred/Mctom/VDB, a CB to replace Maguire's place in the squad, maybe a back up striker etc. are all needed.
Our problem is we can only ever go for the obvious targets who cost an absolute fortune, and we're incapable of negotiating a reasonable price for anyone. So it would be another £200m just to get us the striker, midfielder and goalkeeper. And realistically, I don't think that would be enough to actually go all the way and win it as I said because it still leaves an incomplete squad which would end up falling short to City.
The reason I'm not that convinced we're only 2-3 of signings away is we still can't actually pass or retain possession of the ball. That suggests the whole squad is severely lacking in technical ability which is not something you can fix in 1 window. You're not winning the league if you can't retain possession.