A B777-200 HAD THE AFT LAVATORY VACUUM SYS DEFERRED AS INOP PER THE MEL. DURING FLT; AFT LAVATORIES BECAME UNUSABLE. DIVERTED FOR PLANE CHANGE.

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WE DEPARTED ZZZ1 WITH THE AFT LAVATORY VACUUM SYS DEFERRED 'LAVATORIES NOT TO BE USED BELOW FL180.' ABOUT 2 HRS INTO THE FLT; CABIN ATTENDANTS RPTED SOME LAVATORIES WERE NOT PROPERLY AND WERE FILLING UP WITH WASTE. I HAD A PLT ON REST BREAK GO THROUGH THE CABIN AND INVESTIGATE THE PROB. AFTER MESSAGING MAINT CTL WITH THE PROB AND FURTHER CHKING IN THE CABIN; WE DETERMINED THAT ALL THE LAVATORIES ON THE AFT SYS WERE NOT FLUSHING PROPERLY. THEY WOULD DRAIN LIQUID BUT THERE WAS NOT ENOUGH VACUUM TO COMPLETELY REMOVE THE SOLID WASTE AND THEY WERE CLOGGING UP. WE COMMUNICATED WITH MAINT CTL AND DISPATCH AND WITH FURTHER INVESTIGATION DISCOVERED THAT ALL THE WORKING LAVATORIES WERE DRAINING INTO THE SAME HOLDING TANK AND IT WAS FILLING AT A RATE THAT WOULD HAVE IT FULL BEFORE 1/2 THE FLT TIME TO ZZZ2. AFTER CONSULTING WITH MAINT CTL AND DISPATCH WE DIVERTED TO ZZZ. WX CONDITIONS AND RWYS AVAILABLE AT ZZZ MADE MAKING AN OVERWT LNDG AN ACCEPTABLE OPTION. I MADE AN OVERWT LNDG RWY 9R ZZZ AND PARKED WHERE THE ZZZ STAFF WERE READY TO ACCOMMODATE OUR PAX WITH A NEW ACFT AND CREW. COM WITH THE COMPANY WAS GOOD -- MAINT CTL IN DETERMINING THAT THIS WAS A PROB THAT COULD NOT BE WORKED AROUND AND ALLOW CONTINUATION OF THE FLT; AND DISPATCH IN COORDINATING THE DIVERSION; AND BOTH IN THE DECISION THAT THE OVERWT LNDG WAS AN ACCEPTABLE OPTION.