Maintenance & Pruning
Remove dead stems
The areas circled in yellow appear to me to be old dead stem material - remove them
Take a sharp knife, or a razor blade, or a pair of sharp scissors and cut the stems where I have indicated with the red lines. Cut where the stem is still green. Plants produce a type of scab where they are damaged, which seals out dirt and rot from attacking the stem.
Leave any and all roots, even if they are just attached to a tiny bit of stem. Cut off the stems which are only attached at their bottom end, and gather them all up and put them in a pot. You don't need to root them in water first, they will root just fine in potting mix. I rooted so many cuttings in water just because I tended to cut one or two at a time and didn't have enough to fill a pot. The monster should give you enough cuttings to make up a decent sized pot.
Soil layering - a good way to start and thicken plants
Starting a plant from a cutting is a time honored way of propagation, but it is not the only way. Any time you separate a plant from its root system, it takes a while to develop new roots. It often takes a year or more to establish a new root system, and plants will put on very little foliage while all their growth energy is directed toward new roots.
Vining plants like philodendrons or pothos develop small rootlets at every leaf junction. In their own natural wild habitat, they will crawl along the ground establishing new roots every few inches along the stem. Cultivated indoor plants are often arranged so that there isn't much dirt around to sink new roots into. They are either allowed to let their stems hang downward, or trained into an upright position by being staked.
A good way to thicken a plant which only occupies part of its pot is to lead some of the vines back to the dirt, and pin them so the new rootlets contact the dirt. Once the rootlets sense moisture, they will start growing and anchor the vine to the dirt where it touches.
One of the best ways to anchor the vine is to use wooden toothpicks or small bamboo skewers. Lead the vine to the dirt where you want it to take root. It can be in the same pot, or a different pot. Put one toothpick at an angle into the soil holding down the vine, and put the other one crossing the first one at a right angle so they form an X over the vine.
This stem could be twisted back toward the center of the pot, and staked down to the dirt. In time, it will take root and begin to fill in the pot. Stems can be staked down to any open bit of dirt, and can be weaved back and forth across each other. I have basically covered the entire surface of some pots by doing this, and when the growing tip is trimmed off, the plant will put out lots of new shoots from the old leaf junctions.
Make sure there are starting rootlets in contact with the soil where you stake it down.