I have a shoulder rig with XH-A! ,7"monitor,uhf receiver, and led light box, ext mic.
I like to be able to mount a battery/connector box on the back plate to"power everything" on the rig.

Is there a way to do this with the different voltages/plug types etc.

thanks,
Jeff

Was this a stupid question?

Nope but there are things to consider in trying to do this.
First you need to figure out if the Canan camera can be powered by something other than the stock type battery. Remember that the camera might take say 7.2 volts and an anton Bauer will producr 12 to 14 volts so you'd need a cable to go from the AB battery (using it as an example, there is also V-loc type but same principle) AND a voltage reducer so you don't do damage to the camera. Assuming you're using an AB battery the mounting plates I've always used in the past had a single power tap so you'd need to order and multi tap attachment (AB does make them) attach that to the power tap in the battery mounting plate then run the cable with power reducer to the camera, run another cable to the light whihc in most cases will take the 12 volts power and then another cable to the wireless receiver which again might require some sort or power reducer depending on the manufacturers specs.
Then you need to find the right mount to put all of this on. Westside AV has some really nice decent'y priced gear and are sponsors here at DVi as well as Olaf being a wonderful contributor. It is just one of many that offer gear like the should mount.
When I ran full sized cameras not all that long ago, the AB battery powered the camera, In most cases the wireless ran off a Hirose connection on the camera and the light was either plugged into the power tap on the battery plate or in the case of every Sony FS camera I owned there was a power tap on the side of the camera and I'd plug into that. No as many wires hanging off the camera.
Today using small form factors I use a light that is powered by AA bateries that is sufficient for my work, my wireless also runs off of AA batteries and is either clipped to a bracket on my tripod or hooked to my belt and I use 5 foot XLRs to get from the receiver to the camera OR if I'm on my DVMultirig I can attach the receiver to the back on a plate made for mounting receivers.
There are options it just depends on how much you want to spend and whether or not it would be a benefit to you while shooting.
I think you should do some research at Anton Bauer, B&H, IDX etc and see if the cost would be worth it.
Good Luck.

Thanks Don Bloom for taking time to reply.
I will check out your suggestions.

My main goal was to not have to charge and keep track of so many different batteries. Depending on batteries during wedding shoots has always made me feel uneasy, especially the "off the shelf" batteries used in the uhf unit.

Jeff

Yeah I always liked only charging 1 type of battery but honestly it's not a big deal for me to charge what needs to be charged and change what needs to be changed. For instance generally about a day before a scheduled shoot I'll throw all my camera batteries on chargers to "top 'em off" as I always make sure the batteries are charged since last minute calls aren't uncommon. I have multiple chargers so it's not a biggie. I also use rechargable AAs in my on cam light and have multiple sets so I make sure those are always topped off as well. As for my wireless gear, the stuff I currently use which is AT, everything is run off of AAs so I go to Costco get Coppertops (have used them for about 11 years can't make myself switch) get a package of 40 which gives me enough to switch out all batteries before every job. Old school thinking but worth the peace of mind. I don't care if they have 1 hour of use or 6, they go to my grandkids for their battery operated toys so my son and his wife save a few bucks and I'm not lttering up the landfill. The package is cheap enough so my cost isn't as high now as it used to be and I have only had 1 battery in the last 5 or 6 years that blew out on me.
Everyone has their own system, this is mine. Feel free to use it or not but I can say that trying to run everything off of 1 battery can be more hassel than it's worth.