I'm not sure from your questions whether you are working with a Realtor or have a Real Estate Attorney. Either way you are putting yourself at risk of having accepted offers on both properties.
This could lead to some messy legal ramifications. As the other agent said, you should get some legal advice.
I have prepared offers for my Buyer clients on more than one property, but held the others back until we knew whether #1 offer was accepted or rejected. Then moved on to #2. I would never want to put them in jeopardy. Good Luck on your search.
Wish you great success in finding your perfect home and I would advise you talk with your Reatlor about your concerns here.