Dividing the aglaonema is the most common way plant growers propagate their plant. It is most manageable for plant owners to do.
The process can get messy, so make sure you are outside if the temperature is not too hot or cold for the plant. Doing it inside is the best option for the plant's health, but can get messy.
To divide your aglaonema:
You will need a tarp or covering and a sharp, sterile knife.
Make sure you have enough containers available to repot the "new" plants from the division. I don't know the size of your plant, so you need to guesstimate. From your question, it sounds like many "new" plants will be the outcome.
Spread out a tarp or covering to protect your floor or table for easy cleanup.
Look over your plant and locate various points you plant is coming up through the soil.
The plant propagates itself by suckers underneath the soil’s surface. Its container fills up with young suckers rapidly.
That is okay because it's a positive sign of having healthy plants present.
Now, carefully separate your plant from its soil, and put its container to the side.
Since your plant is rootbound, take a sterile, sharp knife and cut the massive root into several sections for replanting.
Make sure to each section you separate retains a set of even amount of stalks with leaves.
If the soil seems loose enough, gently dust it off with your hands to expose the roots, carefully pull the roots apart using your hands and fingers.
Once you evenly divided the plant, you repot each "new" plant in a new container and new soil.