The short answer is, no, not directly. But... it can be accomplished once you understand how the StudioLive mixers work and consider what you're actually doing in Studio One.
The first thing to consider is that the StudioLive mixer is not just an ordinary audio interface. The confusing part comes mainly from the fact that the StudioLive mixer does not have software/driver output channels that go directly to the physical outputs (like an ordinary audio interface). When you output from Studio One (or any other software) to the StudioLive output 1 ("StudioLive Ch 1" in Studio One), you are sending output to Channel One on the mixer.
When using the 16.4.2 mixer for example, you have software outputs 1-16 which go to Channels 1-16 on the mixer, and then you have an additional stereo output 17/18 which goes to the 2Track In digital return on the mixer (usually used to send your Studio One Main mix to). In other words, there is no way to send audio directly to an Aux bus. In order to have audio from tracks in Studio One go to an Aux output on the mixer, you must send audio output to a Channel on the mixer, and then send that channel to the Aux mix.
So, knowing this fact, there are basically two approaches to doing monitor mixes when using Studio One and a StudioLive mixer.
1) You can set each Track in Studio One to output to its own individual Channel on the mixer. When you use this method, you do both your main mix on the mixer itself, and your Aux mixes on the mixer itself, by sending your mixer Channels to the Auxes.
2) You can set up bus sends on each Track in Studio One to use as monitor mix buses, and have those buses output to Channels on the mixer, which in turn you would send to the Auxes.
Monitor Mixes on the mixer itself
To do your monitor mixes on the mixer itself, you set each Track in Studio One to output to its own individual Channel on the mixer...
...and then you do both your Main mix and your Aux mixes on the mixer
Monitor Mixes in Studio One
The alternative is to do all of your mixing "In the Box" inside Studio One, including your monitor mixes. Using this method, you have all channels go to the Main bus in Studio One
Next, create mix buses (and rename them if you want)
And then create bus sends on each channel for monitor mixes in Studio One,
You also need to create outputs for the mix buses so you can set those mix buses to output to mixer channels
Next, on the mixer you will send just the channel pair for each mix to just the Aux pair that you want each mix to be on.
For instance, in this example you would set Mix 1 to output Ch 1/2 in Studio One which goes to channels 1 and 2 on the mixer. You turn the Firewire inputs on for channels 1 and 2,
you stereo link Aux 1 and 2,
and then you send just channels 1 and 2 to the stereo Aux pair 1/2, as well as pan channels 1 and 2 hard left and hard right in the Aux 1/2 mix. Then just repeat the same concept for Mix 2 and Mix 3 using Auxes 3/4 and 5/6
You'll notice that in either approach, to get individual mixes out of the Aux outputs on the board, you have to set up Aux mixes on the board. The difference is whether you're making the full aux mix on the board like in the first example, or you're doing the aux mixing in Studio One and just sending the monitor mix bus outputs to a stereo pair of channels and then sending that to the aux mix.
These are just two examples of the possibilities, but once you understand how the StudioLive mixer works, you can adapt either method (or combine both) to suit your needs and workflow.