You could do it, it'd be a bad idea.
Both Depo-Provera and the Pill are designed to alter the hormone balance in your body so that it will not be a hospitable climate for fertilized eggs to implant and grow. Both of them do this by adding additional hormones (primarily estrogens and progesterone) to your bloodstream.
I don't actually know the specifics of what happens when the two drugs are combined -- I'll try to find out though -- but in general, the more hormones you add to your body, the bigger a risk you have of causing a severe and unpleasant hormone imbalance for yourself. Depo-provera actually does this all by itself for a lot of women who take it, and the side effects can be very unpleasant.
When you alter your hormones significantly, two things can happen:
1) you'll get side effects of having imbalanced hormones
2) your body will try to adjust by pumping out other hormones to try to balance out the pharmaceutically-added hormones, thus worsening the hormone imbalance
Either way, it can be unpleasant and possibly really bad for your health.
Combining multiple hormone methods of BC also won't be any more effective than using one hormone-based method. It could potentially be less effective, if your body tried to balance out the hormones as in case 2) above. It would probably also make you ill.
Better you should combine a hormonal method of contraception -- Depo or the Pill, whichever works for you -- and a BARRIER method, preferably condoms. Why? Well, not letting sperm get in there is a great contraceptive, first of all, and second of all, you should only be having sex with condoms ANYWAY, because only barriers can prevent you from sharing bodily fluids. And not sharing bodily fluids is the best way to prevent yourself from getting HIV/AIDS and many, many other Sexually Transmitted Infections.
Condom + Pill or Depo = Good Idea!
Pill + Depo, no Condom = BAD idea, for more than one reason!
Associate Editor, Scarleteen
"Be Excellent To Each Other" -- Bill and Ted