Not really a good comparison for division (pothos vs peperomia). The answer is "probably yes" but the plant is terribly fragile and you could expect a degree of collateral stem and leaf damage. You could saw right through the rootball with a sharp clean knife - however until you remove it from the pot it will be difficult to know exactly where to do that. You would need to try to disturb the plant and the roots as little as possible and preferably make it a 2-man job with someone holding the plant and then dropping one half into a new pot and you backfilling. However, since it is such a nice plant right now, and set-back is probably likely, why not simply move it into a larger pot if you think it is cramped?

http://forums2.gardenweb.com/discussions/1498394/sunburned-leaves?n=35

How do you determine when it's time to water? It looks like the result of excess water in the soil for extended periods; and, a high level of dissolved solids (salts) in the soil might be a contributing factor. When your soil is too wet, it limits your plant's ability to take up water, which results in a drought response. The first thing most plants do when threatened with drought is start shedding leaves to conserve water, even if the roots are drowning in a sea of plenty. Too, high salt levels in the soil work in combination with an excess of water to further limit water uptake. Enough salt in the soil can actually reverse the movement of water into cells and actually pull water out of cells (reverse osmosis) in exactly the same way that curing salt pulls moisture from meats like ham/ bacon/ jerky, ..... When you water, you should water thoroughly, so at least 15-20% of the volume of water required to fully wet the soul exits through the drain hole. Then, the plant should never sit in the effluent (water that has moved through the soil and out the drain). That practice provides a pathway back into the soil for all the salts that were flushed from the soil when you watered. In passing, it should be mentioned that root congestion causes loss of older leaves, as does decreasing light levels, but given the rotted appearance of the leaf stems, I'm thinking your issue is related to poor root health. You might lift the plant from the pot and inspect the roots to see what condition they're in, and start using a 5/16" wooden dowel rod (any hardware store), sharpened in a pencil sharpener to test the soil's moisture content. Stick it deep into the pot. If it comes out wet or stained dark from the soil, withhold water until it comes out almost completely dry. There will still be sufficient available water at that point to satisfy your plant's need for moisture. I think you'll find the info below to be helpful. Growing Overview Sick or Dying Plants? Al

i left it on the deck for a few nice days and this brown appeared (assumes maybe bacteria?) and it started dropping those leaves. ==>>> explain what happened ... i would probably rule out a cold event in CA ... did it end up in sun ... if so.. sunburn ... whatever happened.. to injure the leaves.. the plant is taking care of it.. by shedding them ... i wouldnt really care what happens to a damaged leaf after damage.. meaning... it doesnt matter if it bacterial.. etc.. there is really nothing to fix at this point ... and if its releafing ... it sounds like it isnt struggling.. so again ... whats to fix??? just a WAG .... im going to guess that you might be loving it to death by overwatering .... it looks sodden in the pix ... probably because you just watered it.. but let it NEAR dry.. before watering again ... and if g ma had a huge plant.. was her pot as small as yours ???? just dont stress about it ... if its been in your family for years and years.. it just cant be that tricky ... sorry.. i cant ID it ... ken