I have talked to an attorney about this specific question. The answer is no, you can't write multiple purchase agreements on multiple properties.
If you want to speed the process, have your agent put language in the purchase agreement that the seller must respond to your offer within 48 hours or the offer is null and void.
The 'three day rule' applies to purchases made on the internet. Unless there is specific language in your purchase agreement, (in the form of a contingency) there is no such thing as a 3 day grace period.
Frankly if I were a seller, and I had multiple offers on a property, and your offer had the 48 hour contingency or the 'we're writing multiple offers' contingency, your offer would go to the bottom of the pile.