Modifying an existing chip is pretty much impossible. Chips contain structures on multiple layers, but you can only really work on the topmost layer directly. There also usually aren’t really unused gaps, components are placed as tightly packed as possible because if you can make the chip smaller then you can get more chips out of each wafer (because manufacturing costs depends mostly on the amount of wafers and amount of layers on each wafer, not on the amount of chips per wafer).

I guess in theory you could grind the old circuitry off the chip to then build up new circuits on the old chip, but that’d be much more challenging than starting from a new wafer and also not really offer up any benefits.

As a conventionally understood process, no, and there is no practical way of even considering what you’re suggesting as a hypothetical. Maybe I and everyone else who knows anything about this topic are wrong though. If you can figure out a way, prepare to be very, very popular, because it would legitimately be a game-changer.

The only thing I can vaguely think of fitting what you seem to be asking about is the process of combining hundreds or thousands of old pieces of hardware to run tasks in parallel. For example, think of turning a whole room into a cluster of Commodore 64s. If you had 1000 C64s, you could in theory run things 1000x as fast as a single Commodore 64. That’s an interesting idea, in theory.

As far as catching up to Moore’s law, it’s going to be a struggle: This is almost never energy-efficient and almost never practical in the extreme, but it can technically be accomplished. Running tasks in parallel like this across different hardware is also extremely limiting though, as the isolated tasks have no way of communicating with or sharing information with each other at anything even close to the speed of actually processing the information. This is fundamentally different from a single-threaded task running at high speed on a single, combined processor, and requires careful design in either chunking the data into 1000 totally independent pieces or pipelining it into 1000 equally-computationally-intensive steps to be performed or some combination of the two, things which can really only be done effectively in certain problem spaces. This is why multi-threaded tasks typically end up not scaling up linearly in speed as you throw more cores at them. Many problems are not effectively parallelizable and cannot be cleanly broken into chunks without losing the context they need and cannot be split into so many discrete steps while maintaining the predictable timing window needed to schedule those tasks into a pipeline that isn’t constantly waiting on a handful of “slow” steps. It’s a huge challenge and not a realistically solvable one.

If you just want homemade processors that can technically accomplish the same things as modern processors, sure, that’s technically possible but it’s going to be really, really slow and impractical. If you want homemade processors that can do a very limited set of things at something resembling Moore’s law speeds, you might be able to pull that off for certain very specialized tasks but again not in a super practical way and likely not in an energy efficient way either. What you almost certainly can’t do is both of those things at once. You can’t have the full capabilities of a modern processor in a homemade processor that is also as fast as a modern processor. That would just be a modern processor. And those are unbelievably advanced devices, they are basically the pinnacle of humanity’s collective technological achievement. I don’t think anything else can really compare to them, and you absolutely are not making them in your garage.

Are you asking if a hobbyist can open up an old cpu and add parts to it to make it faster?

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.

No, it would not be possible, the etching process would destroy extant features on any silicon. There are multiple steps to it and some will destroy the work of the steps that come after, so putting a finished chip through would remove the existing features.

Generally fabrication is done on a circular 300mm wafer, printing a grid of identical chips on it that are then cut out. It would be highly inefficient to do each chip one at a time, doing one small chip or 50 chips at once on one wafer takes the same amount of time and effort.

And the bare silicon left after the first few steps isn’t really worth much. You can go buy a blank high end 300mm wafer for like 81 bucks online. The material value of the silicon is nothing compared to the value of the machine time.

Hypothetically, it might be possible, but there aren’t practical gains to be had from it. Easier to fabricate a new chip.

The optimal design is unlikely to be a straightforward modification of an older chip.

Even if it were, modification would add more variables, where we’re constrained by yields today.

And our processes today aren’t designed for it.

EDIT: That being said, you might be able to repurpose an older chip in a piece of electronics that uses multiple chips in a situation where you’re unable to get the older chip for some reason. I can’t think of many scenarios where that’d be economical, but hobbyists have certainly reused components from older electronic devices.