I am no stranger to multiple GPU set-ups, but as of lately I'm having troubles on a Win8.1 box. It started thus:
After an update BOINC would no longer work with my two GPUs. I could use my nVidia GPU or my Ati/AMD GPU, but not both -as I did before. As long as BOINC did not run all was fine and I could use two monitors, each connected to a different card. As soon as BOINC started the machine would just reboot.

Then I upgraded the CPU to an i7-3770 with built-in HD 4000. Now I can only use the HD 4000 because adding either the nVidia card or the Ati/AMD card results in rebooting, even when I disable the HD 4000 -but only as soon as BOINC starts. I can connect monitors to each card when not running BOINC and have them working right along each other. I do have a cc_config.xml with

<cc_config>
<options>
<use_all_gpus>1</use_all_gpus>
</options>
</cc_config>

,otherwise I would not have been able to use both nVidia and Ati/AMD cards along each other in the past.

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The computer rebooting points to me in either of two, maybe three directions:
1. Unstable Windows.
2. Underpowered Power Supply Unit.
3. Broken motherboard.

So start off with Windows Event viewer and see what's in there, any warnings, any explanation? Perhaps some BSODs that you don't see due to having set Windows to reboot immediately upon getting to a BSOD. You can use Blue Screen View to quickly show the latest BSODs.

What brand and model PSU do you have? Can it output the amount of required Volts to power two or three GPUs? Can you try with a spare PSU?

The last thing is difficult to test, but shouldn't be dismissed. Micro-fractures in the connections on the motherboard can be attributed to what you see. Normal under normal circumstances, but rebooting as soon as you put some load onto it.

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No warnings in the Windows events viewer, one OCZ 500 Watt PSU died on this motherboard, I replaced it with another 600 Watt PSU. Problems ever since.

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Your GPUs are what versions?
When the previous PSU died, did it go with a bang and magic smoke? Or did it go quietly, one day you turned the computer off, the next day it wouldn't restart?

If with a bang, your motherboard may have taken a hit.
If any of the present GPUs were attached to it at the time, they may have taken a hit.
The PSU itself may be having a problem. If still under warranty, I would go back with it and have it replaced, just to be sure.

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The GPUs are a EVGA GTX 650 and a Sapphire HD 7790. The 500 Watt ModXStream-Pro OCZ PSU died after a Win8.1 update, it just did not come up again. It had been running a few years 24/7 and was past warranty (OCZ have since stopped making PSUs altogether).

Both GPUs still work (using the 600 Watt PSU) and could run BOINC when the system still had its i3 2100, but not together anymore. In the past they had that problem too when the Intel OpenCL drivers (for the i3 2100 and it's HD 2000) were installed. Uninstall of the Intel drivers and disabling the IGP was enough to have both nVidia and Ati/AMD cards running together. After the dead PSU I could install the Intel drivers to no effect on BOINC and enabling a 2nd monitor on the HD 2000.

When the i7 came in with it's own crunching capable HD 4000 the computer would reboot when combined with either discrete card -as soon as BOINC starts. Uninstall of the Intel drivers and disabling the IGP now does not result in having a running discrete card in BOINC. Not running BOINC results in having all active video outputs active, running BOINC at the moment is only possible on the HD 4000.

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