I am a graduate. I accepted an offer one month ago and the company is still carrying out background check. Today I received a better offer and I realised the company is also using the same background check agency (First Advantage). If I signed the second offer without rejecting the first offer, I am wondering if both companies would be able to find out that I signed two offers? The reason why I would do this is that my second offer is conditional. Or should I reject the first offer first before signing the second one?
I can only guess here, as I am not associated with "First Advantage". But cashing in twice about the same work, sounds like a good thing (for "First Advantage").
However you never know what happens there and what agreements are in place. If you would be open to all parties, that you are currently comparing offers, this would be just fine.
From the legal point of view, if not agreed on otherwise in terms and conditions, your private data (including where you apply) must not be shared with third parties. In each case, the other employer is a third party. This is due antitrust/cartel laws in most jurisdictions.
Basically, you need to trust the process, but there is a chance of word-of-mouth.
I once did a background check with an agency and found it quite intimidating.
Forget about the background check.
You have two offers, decide which of those offers is best for you and accept only that offer and reject the other one.
If I signed the second offer without rejecting the first offer, I am wondering if both companies would be able to find out that I signed two offers?
Both companies can find out through any number of ways other than a background check. It's not a good idea to simultaneously accept multiple offers. Accept the best offer and move on from the other company.