If you're extremely motivated, love your subjects, and have a naturally great memory then it's definitely possible. But it's not a decision which should be taken lightly.
I would suggest you start by asking yourself why you want to do this. It won't necessarily advantage you in university applications, and most students find A levels challenging and stressful at the normal pace. Assuming you're of the normal age to start A levels (16-17ish), what's to be gained by rushing? Surely you can spare another year?
If you do decide to do it, then being exceptionally organised right from the start will be essential. A lot of A level students take a term or so to get into the swing of it, and as a result tend to underperform in their first year and improve later. You cannot afford to do that - frankly, if you're seriously considering it you should be getting ahead on the content already. Obviously I don't know how talented a student you are, but even the best students aren't immune to underestimating a unit, course, or A levels as a whole. Avoiding this is absolutely critical.
As for how many you can take like this, I think three is the maximum any sane person would recommend. More would almost certainly stretch you too thinly.
Good luck whatever you decide to do - for what it's worth I have experience self-teaching at A level and I have an offer from Cambridge, so if you have any questions feel free to quote/PM me!