using 512mb ram modules in a beige g3

It's possible but it will only read half of it.

I thought the issue was with the 16 chip limit- so if it has 16 chips wouldnt it be able to run?

Well maybe, but my 512MB sticks have 16 chips and they only show up as 256MB...

I'm too lazy to Google the technical reference up again (Among other places it's in one of the "Power Macintosh G3 Developer Notes"), but basically the Motorola MPC106 ("Grackle" in Apple-centric technical references") memory controller used in both the Beige and B&W G3s has a physical limit of 1GB addressable RAM space. Furthermore, that 1GB of RAM space is broken into 16 banks, each of which has a limit of 64MB. A single DIMM socket can have 1, 2, or 4 banks of RAM, depending on the organization of the individual components, but the *maximum* size of a bank is 64MB. That's why only "double-sided" (16 chip) 256MB DIMMs work, because said DIMMs consist of four 64MB (the maximum size you can have) banks. DIMMs with single banks larger then 64MB either won't work at all or will be seen as some smaller size. (Not *necessarily* half size.) So at best a 512MB DIMM will show up as half size.

So that's it. You can't have more then 64MB of RAM in a bank, and you can't have more then 16 banks. (12 in a Beige G3, because it only has 3 sockets, not 4 like a B&W.) The only way you could make a 512MB SIMM work to full capacity would be to devise some sort of adapter which bridged two adjacent SIMM sockets and contained circuitry to remap its larger banks into 8 smaller ones. Wouldn't be cheap, and it would be sort of pointless since the end result doesn't actually raise the amount of memory you can put in the machine.

--Peace

(Edit: I found the technote explaining this here. It's the .PDF, and updated accordingly. Look at the section about RAM DIMMs. Unlike some Apple documentation which understates the capabilities of their systems this is an accurate description of the device's capabilities. If you look hard enough you can find the Motorola documentation for the MPC106 and confirm.)

Would it be feasible to add an extra socket to the beige?

No... there's no room for another socket.

It actually would fit you'd just have to elevate it above the other circuitry