Is it possible to run a Rode shotgun mic that is 3.5mm and Sony ECM-AW3 wireless bluetooth mic that is also 3.5mm together at the same time on a Canon Vixia HF M32?

Maybe some kind of splitter or something?

There are boxes made that do this, I have owned and used them, but forget the brands. They attach to the bottom of the camera and then can be mounted to a tripod if necessary. They are slightly cumbersome but effective.

There are two popular brands. Go to the audio forum and start a thread there. These units allow you to control volume for each channel.

I would think you could use a splitter, don't know, but you would have no control over levels, and I'm not sure it would be a great way to go, but maybe you could make it work.

In the end, it is obviously much better if possible to buy a XA10 with it's two XLRs.

Zoom makes a recorder for about $100 that syncs perfectly with video. Buy a Lavalier mic and you could skip the wireless. I use one for every wedding and the quality is superb, as good as my $500 Sony Wireless unit, if not better.

Jeff, are you talking about Beachtek and Juicedlink?

Beachtek, Juiced and Studio 1 are some brands. There are others in the general class of field mixers.
XLR Adapter - Camcorder XLR Audio Adapter for a Video Camera (http://www.studio1productions.com/xlr-menu.htm)

One issue with using different mics is matching levels. Use of AGC can be especially "dangerous" to your sound because you may get unwanted side channel effects where the level in one channel effects both in strange ways not as apparent with typical stereo sources.

That's right D.J..

I think something like this is what you are looking for.

For only $0.26 each when QTY 50+ purchased - 3.5mm Stereo Plug to 2 x 3.5mm Mono Jack Splitter Adaptor - Gold Plated | 3.5mm <--> 3.5mm Adapters (http://www.monoprice.com/products/product.asp?c_id=104&cp_id=10429&cs_id=1042901&p_id=7205&seq=1&format=2)

Downside is that you will not be able to adjust the gain independently for your mics in the camera, but it may not be an issue.