Short answer: it is possible.
Longer answer: it's possible, but few people attempt it, and few people succeed in it. The trouble with studying A levels outside school is that you have to be very dedicated and motivated. No teacher is setting you homework, so there are no repercussions for letting things slip. Without the school framework, it's more likely you won't be prepared for exams in time. That said, I'm teaching myself 2 of my 5 A-levels, and if you're conscientious enough it's almost preferable. You can move at a faster pace, have a greater sense of achievement, and often have a better understanding of the basic principles at the end.
However, unless you are extremely (extremely!) bright and quick, I think seven with two outside is too many. AS levels require a lot more time than GCSEs, and I would expect you will get very stressed very quickly if you tried to take on too much. Better to choose five in school, give it a month or two of study to see how you cope with the jump, and if you still are really sure you could manage, start on an additional one. I wouldn't do Eng Lit outside school though, unless you have a very kind teacher willing to mark all your essays :P