Can I inherit a contract above my warrant level?

Sure.  What is the problem?

It's up to the agency issuing the warrant.

FAR 1.602-1(a).  "Contracting officers have authority to enter into, administer, or terminate contracts and make related determinations and findings...Contracting officers shall receive from the appointing authority (see 1.603-1) clear instructions in writing regarding the limits of their authority."

Yes, read your warrant and follow the limitations. This is a frequently asked question. "My warrant is $1M. Can I signed a $500K modification on a $10M contract?" Yes, you can, unless your warrant states otherwise. Usually, the dollar thresholds are based on the contract action, not on the underlying contract's ceiling value.