I did a course in photolithography, including a lab session where I literally made an unpackaged ASIC by hand, using technology that was current in the mid 90s. Etching silicon and doing photolithography is completely out of the reach for a hobbyist, even from scratch, even with 30 year old technology. Reusing a random chip and adding to it is simply impossible.

Essentially, you are looking at the following problems with simply creating a new chip:

1. Need access to a large clean room
2. Need a furnace that can heat up your silicon wafers to silly temperatures in order to do doping via sputtering.
3. Need chemical handling equipment, including safety gear required for handling hydrofluoric acid.
4. Need a photolithography device with your designs.
5. Need to cut, test, and package chips after they are created.

And the additional problems with using an existing chip:

1. Need to decapitate the existing chip and remove it from the package.
2. Need to work with a single already sliced chip instead of a wafer.
3. A completed chip will have metal vias that cover a large portion of the silicon, you would need to perform your chemical etching without harming these or any silicon that has been used.
4. Generally, Asics don’t have wasted space, but simply larger components. There would be no footprint available for your design, even if your hobbyist tooling was smaller than the one used for the components, which is probably wouldn’t be.