That is not necessarily true, not sure where Chris got this. Unless that is specifically stated by the seller there is no law that says you can't make an offer on a home that is already in contract. A seller can accept as many offers as they want.
Have your agent contact the seller to see if they are still accepting offers.
In the event there are multiple offers all ready and your offer would be number 8, to present an additional offer would likely be a lesson in futility. The listing agent may be able to advise you on the best course of action.
Imagine what you would feel like if two of your backup offers were accepted while you had another accepted offer in play. It could stretch you resources too far.