Early Decision

Only a handful of osteopathic colleges have ED: COMPacific; Michigan State; Kirksville; PhiladelphiaCOM; TexasCOM.

You can apply ED to both osteopathic and allopathic schools at the same time because there is no communication between them.
However, I think there is one reason not to:
it is unethical.

In any case, you MUST take the April MCAT, unless you have taken an earlier one and had 30+ scores across the board. You MUST have your application completed and in apple pie order and your recommendations available very early.

If you apply EDP, you may not apply to any other med school until after a decision is made. If you are accepted EDP, you MUST attend. if you decline, you cannot apply to any other medical school in the same year; you must wait until the following year's application cycle. AMCAS tracks this.

If you are a strong enough applicant to be accepted early decision it is probable (though by no means certain) that you would be accepted in the non-EDP pool. You will be screened early in the application cycle (but after EDP candidates are decided upon) and have more options of where to go.

Unless you are really a strong candidate, and you want to and will go to the med school if it accepts you, I would not encourage you to apply EDP anywhere.

Make an early decision if you want to go the early decision route.