AN ACR LTT CREW FLEW AN ACFT THAT WAS PAST ITS MAINT DUE DATE.

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I AM FLYING A BEECHCRAFT 1900. WE HAVE RECENTLY CHANGED OUR ACFT INSPECTION PROCS FROM HRS UNTIL INSPECTION IS DUE TO EXPIRATION DATES. MY FO AND I FLEW 3 AIRPLANES TO COMPLETE A 4 LEG DAY TRIP/2 OF THE ACFT WERE ORIGINATORS THAT REQUIRE A RUN-UP. THE TIME BTWN ACFT SWAPS WAS MINIMAL AT BEST AND WE WERE RUSHED. THE NEXT DAY; I RECEIVED A CALL FROM THE CHIEF PLT WHO INFORMED ME THAT 1 OF THE ACFT THAT WE HAD FLOWN EXPIRED FROM INSPECTION THE DAY BEFORE; AT MIDNIGHT. THIS ACFT WAS FERRIED TO A MAINT BASE FOR INSPECTION LATER IN THE DAY. LACK OF TIME BTWN ACFT SWAPS COMBINED WITH LONG DUTY HRS PRIOR TO THIS INCIDENT CONTRIBUTED TO ITS OCCURRENCE. BEING DISPATCHED LIKE A 121 FLT; MANY PEOPLE INCLUDING MYSELF; COULD HAVE CAUGHT THIS PROB BEFORE IT OCCURRED. I BELIEVE THIS SIT COULD BE AVOIDED BY ALLOWING MORE TIME FOR CREWS TO INSPECT THEIR ACFT PRIOR TO A DEP TIME. SUPPLEMENTAL INFO FROM ACN 288371: I FLEW INTO LGA AND WAS INFORMED BY OPS OF AN UNSCHEDULED ACFT AND TRIP SWAP. WE HAD LITTLE TIME TO PREPARE THE NEW ACFT FOR DEP AND DEPART ON TIME. IN SHORT WE WERE RUSHED FOR TIME. THE CAPT AND I BOTH OVERLOOKED THE FACT THAT THE MAINT EXPIRATION DATE HAD RUN OUT ON THE ACFT. SINCE WE ARE PAST 121 DISPATCHED OUR DISPATCHER AND MAINT SHOULD HAVE RECOGNIZED THE FACT THAT THE ACFT SHOULD HAVE BEEN GNDED. THE CAPT AND I SHOULD HAVE SEEN THE EXPIRATION DATE ON THE MAINT LOG.