Are you talking about the Trim Monitor or the Source Monitor?
Source monitor. Thanks for asking.
Thought that might be the case...
Unfortunately, this is a big "miss" in Premiere Pro--multichannel assets can't be previewed with all channels. More specifically, you can't preview more than one channel at a time. In the Source Monitor's Audio Waveform view, however, you can select one of the channels (labeled "Track" there) to preview from the Track dropdown. Sadly, this isn't sticky, so you have to change it from clip to clip--it's very annoying. I'd suggest making a feature request for better monitoring and control of multichannel audio here: Adobe Feature Request/Bug Report Form
My usual workaround is to actually use a scratch sequence as sort of a sandbox for multichannel clips. I drop them all in one sequence, trim and break them up, and rename the clip instances there. I then either duplicate that sequence and use it as a working sequence, or I copy clip instances from that sequence to another. You can also set up a workspace with two or more Timeline panels, so you can easily drag clips from one sequence to another. It's not a perfect workaround, but until we get better monitoring capabilities, it's the best solution I've been able to come up with.
Thanks for the feedback. Your solution is typically my workflow. It's a very rare occurance when I need to hear anything other than Channel 1 audio, just happens to be the case today.
Also, thanks for the feature request link. There are a few things I'd like to see Adobe incorporate. Mostly incorporating P2Card file support in Adobe Bridge.