Four A-levels including Further Maths

I am applying to 6th forms atm so I have to make my A level choices now (one before the end of this month!). I am doing 12 GCSE’s and am currently predicted 8/9 across the board and a couple 7’s (Eng lang & photog)
I want to do Comp Sci, Maths, Further Maths & Physics. With a view to doing either Comp Sci (top choice atm) at uni or Engineering; *maybe* NatSci
All the sixth forms try and get you to stick to 3. They will allow me to do 4 if one is FM but it’s still not generally encouraged.
I am open to doing 3 as I want top grades, but the trouble is I don’t want to limit my options post A-levels.
Dropping physics shuts off pretty much most decent Engineering courses, as well as NatSci etc. Dropping FM means I’m less competitive for top CS *and* Engineering courses - even when not asked for it’s one of the most common A - levels that student who achieve places at top uni’s have. Plus it’s super useful to have for when I actually get to uni as I’m looking at maths heavy courses.
CS is my absolute favourite subject and I got the highest mark in my year by a country mile in our Y10 mocks so I *really* don’t want to give it up even though I know it’s not needed for a CS degree.
I guess my questions are -
Is four doable for an organised, disciplined & hard working human?
Is there enough of a crossover between all four subjects to be beneficial (FM options are discrete & further mechanics)?
Or
Should I bite the bullet and give up one?
I could always start with 4 and drop one…
I guess I’d just like some advice and opinions please from others to help me make my choice!
If you got to the end of this well done and thank you ☺️

A reasonable number of kids do 4 so m/fm/phy/cs when applying to competitive unis for maths/cs/eng/... and places like the maths schools do 4 normally, so it is doable with a bit of organisation. Strictly speaking 4 isnt necessary, and if youre school normally does 3, then thats all that they would assume youd do. However fm is pretty much required at competitive unis, so if youre doing 3, youd have to drop either phy or cs. You could always take 4 in y12 to as then decide if you want to drop 1 in y13. Similarly, some (competitive) places require you to do an entrance exam on top of your a levels so when you decide what you want to do, youd have to factor that in as well.
Id pretty much forget about fm options. They are what they are.

Thanks for your reply.
It’s not that the 6th forms don’t do 4, it’s just not encouraged as they are non selective schools but people do every year. One of them will only let you do 4 if the 4th is FM. It is just because the likelihood of getting better grades from 3.
I’m leaning towards trying 4 and seeing how I get on. If I enjoy physics at A level enough to want to keep it or try with 4 or even possibly drop CS. My physics teacher really wants me to carry on if I stay here and I like the though of keeping options open but my heart is in CS atm.

I agree about the 3/4 view from the school. If youre aiming for a top/competitive uni, Id agree about keeping your options open by taking 4 in y12 and seeing how things go. Also over the summer (presume youre in y11) have a look/think about what supercurriculars for cs might be "required". Cs was stupidly competitive this year and having a decent set of supercurriculars and doing well on the entrance exam(s) were important as well as the a levels.

Yes go for 4.You can always drop one if it gets too much especially as one is FM.Horses for courses as they say.

if you're doing exceptionally well in one a level then you might be able to do 4