Q: Can I add two monitors to a Power Macintosh G3?

Is that what was called a Beige Powermac?

You'd need a 33 MHz PCI video card, but I can't remember if OS9 on those supports multiple Video cards.

OS X did support dual monitors on older Beige PowerMacs as my Beige had a dual DVI PCI card in my beige desktop PowerMac and I used two flat panel monitors on this Mac before I moved to a PowerMac G4 tower and used those monitors with that Mac.

Like you, I do not remember if this dual monitor support was available in OS 9 or not.

I wanna say, yes, as my beige was still a dual booting system using both OS 9.1 and OS X 10.3.8, and I remember still being able to have two monitors become active under OS 9.1. I am just not entirely sure, though.

I distinctly recall using two monitors with my beige G3 and I only had OS9 on it.  Of course you need a second video card  for the other monitor.

All Beige G3s had onboard video hardware in addition to PCI slot, unlike the later towers that had to use PCI cards for all video. So you can attach one monitor to the onboard video (MAX of 6MB VRAM in the ATI 3D RAGE Pro on the logic board) and add a PCI video card for the second. However, the practical limit on monitors is two.

The "elephant in the room" here is that the PCI bus has a limited power budget somewhere around 40-45 watts across all three slots. Even the most simple PCI video cards demanded around 25 watts so having more than one video card was not practical. Still, that gave you two monitors if one did not need super-high hardware acceleration.

I progressed through three upgrade video cards in my Beige G3. The first upgrade was the ATI Rage Orion 16MB, followed by the original ATI Radeon Mac Edition (not the dumbed-down Radeon 7000 Mac Edition), and finally the ATI Radeon 9200 128MB. The latter never played well with OS 9 and did not support Quartz Extreme in OSX, so it was somewhat of a horse designed by a committee, if you get my drift.

The G3 built-in video card has a unique video plug for Macintosh Displays.  Most of the video cards that you can install in an expansion PCI slot are going to have the VGA and DVI ports, and possibly S-video.  I had used a Macintosh-to-VGA adapter to use a VGA monitor (it came with the Viewsonic Display when I bought it) with the built-in G3 video, but I am not sure of an adapter that goes the other way.  I don't know if there was an adapter to connect a Macintosh Display to a VGA port.  I am even having trouble finding a link or image of the adapter that I had to help explain this better.

At one time I had three extended video displays on my G3: a VGA monitor on an adapter to the built-in G3 video card, and with an ATI Radeon, a DVI monitor and an S-video to a VCR/TV.   (The ATI Radeon supports two independent displays, where the S-video can mirror one of the VGA or DVI outputs)

This is what I was talking about, it connects a VGA monitor cable to the G3 Macintosh Display port:

http://www.amazon.com/Adapter-DB15-Male-HD15-Female/dp/B0016OC1J2

Now, they do make some adapters called "Gender changers" so that you might be able to make the reverse of this, not sure if that would allow you to connect the Macintosh Display cable to a VGA port on a PCI card.