Use as example PIC18F45K22 (can work on 1,8V) which have 28 10-bit ADC channels, take values from channels, compare them and some output pin should switch some MOSFET DC channel on, and other channels turn off.
The capacitor automatically charges to whichever is the highest incoming volt level.
This method subtracts a diode drop from all incoming signals. Therefore you should add 0.7 to all of them beforehand, because signals below 0.7 V will get disregarded otherwise.
The transistor can be used to discharge the capacitor. Or install a medium resistance across it, to discharge it gradually.
You could use one op amp precision half-wave precision rectifier for each voltage and connect all the Vout's together (with one common load resistor). The ORed output will equal the highest input voltage.
If you need precision, you can string a bank of peak detectors in parallel. https://en.wikipedia.org/wiki/Precision_rectifier
If precision is not required, and you can roll your own opamp, you could design an opamp with 16 +ve input terminals and get a lousy peak detector.