Non-Sensitive /Low Risk Background Investigation


I have a question…I recently accepted a position (9/11) with the Dept of Ag - Non-Sensitive Low Risk and the the background is in progress right now and has been for about 3 weeks. The problem is, I was recently offered another position (9/12) also with the Dept of Ag - Non-Sensitive/Low Risk. If I accepted that second position, would they be able to continue with the same background investigation in progress since it’s the exact same type or does the process have to start all over again because it’s a new offer. I sure hope not but anyone, please respond if you have any idea. Thank you!