The StudioLive 16 Series III console is still a 32 channel mixer under the hood (17-32 are Digital-only, USB or AVB input), and that is the maximum number of channels you can have, in any configuration (well, you've technically got 38 channels to mix with if you count stereo Aux Ins 1 and 2 and Tape In).
Yes, you can use one SIII 32R (32 analog ins) to feed all of the channels on the SIII 16R (or a mixture of Rack inputs and Console inputs).
Currently, you can only use one Series III Rack mixer in stagebox mode with a Series III Console, so no, you can not use two SIII 16R mixers with one SIII 16 console.
You can use one SIII 16R (16 analog ins) to feed the digital-only channels 17-32 on the SIII 16 console though. Then you'll have 32 channels of analog input, but just physically located in two spots, stage and FOH.
Same thing with an SIII 24R... 24 analog inputs that can feed any channels on the SIII 16R (routable in blocks of eight).
See also the StudioLive Series III Stagebox Mode Addendum