Captain reported a malfunctioning Remote Cabin Sensor already on MEL failed and caused erroneous cabin altitude readings. This caused the passenger O2 masks to deploy and required an immediate descent. The Crew continued to a destination airport.

Narrative

Leaving ZZZ to ZZZZ; the logbook had a deferred MEL 21-26 (Remote Cabin Sensor); also 2 other MELS and more NEFs (Non-Essential Equipment Furnishing). About 7+hr; smooth air; we suddenly got a momentary red 'Cabin Altitude'; that immediately went away. Cabin altitude was steady (5;600 ft for FL350); and no pressure change felt in ears. Following warning; ALL the cabin O2 masks deployed; with advisories. All checklists were accomplished. PAs made. With clearance; we descended to FL140 initially; determined FAs couldn't cover used masks with walk around bottles; then continued descent to FL100 (10;000 ft). Contacted dispatch; and still had enough fuel to make ZZZZ; rather than divert to ZZZZ1. All passengers were fine. Possible problem developing from the placarded/deferred Remote Cabin Sensor; which may have given a false cabin pressure reading; or another related sensor having problems. Spiked reading triggered mask drop. Encourage maintenance to preemptively fix rolling MEL items; and not fly ETOPS aircraft over water that have several MELs deferred.