If you are relying on the equity of your current home to purchase the new one, then you may. Funding on the new purchase has to be fully in place in order for it to close. The only other option I could imagine would be for the seller of your new home to agree to a second mortgage tied to the equity in both homes. They would only do this if they didn't need all their funds and were being compensated for their trouble.
If there is more to your question than I am understanding, please elaborate.