I've been thinking more about this after recently playing with copper pipes and valves.
The way I understand it (as AssafL mentioned recently) to reproduce a truly arbitrary pressure profile would require a gear pump and some kind of feedback system (pressure sensor and electronics to adjust the gear pump based on the readings from the sensor)
A gear pump would be the "stepless" way to do this, but I was wondering if a stepped approach might be worth the effort.
I'm not sure of the total cost of a DIY gear-pump, pressure-feedback system so don't know if this is worth it.

Couldn't one just create different routes from the pump to the boiler with a pressure valve on each path?
You can add a needle valve to one route if you wanted to control the flow.
Then have some solenoids and relays to control the routing.
You would have to "program" the profile by adjusting the needle and pressure valves.
You would have one route for each "stage" of the profile.

Where would this plan go wrong?

I guess it might work.

At the moment the Rocket R60 is a stepped pressure solution, The Advanced Coffee Systems Vesusvius is a gearpump solution.

Your proposed solution/profile has 3 steps?

the ascii art diagram shows 3 stages/steps, but you could arbitrarily add more.
And you can adjust the value of each stage based on the resolution of the needle/pressure valve

On a vibration pump machine, I suppose you could add a second OPV at lower pressure in parallel to the existing one and in line with a solenoid valve. This would be your path for preinfusion or low pressure shot finish. The solenoid would have to be powered on for the time you want to pre-infuse or otherwise reduce the pressure. The ramp-up from LP to full-on extraction pressure should be more or less gradual due to the vibe pump; the ramp-down will be more of a kick-down.

Cool thought. It will mimic line level pre-infusion - but at adjustable pressure.

A few thoughts - simplifications:
You could ditch one of the solenoid valves (the one on the needle valve line - since it is always the slowest).
You could also ditch one of the pressure regulators - since the pump is regulated, so the bottom line needs no regulator.
Also, on the needle valve - the pressure regulator - if needed - should be on the inlet side of the needle valve. But if you use a high pressure needle valve (like you have on your plumbing exercise) - you don't need a regulator there as well.

So a flow controlled line: Needle Valve only
A preinfusion/postinfusion line: Valve + Regulator
A full pressure line: Valve Only.

One can extend this further by "linearizing" the ramp up by using an E61 style pre-infusion spring (like Kees uses) on the regulator line.

The only question now is if this would be even worth the effort.

I've seen flow profiling (fp) vs pressure profiling (pp) threads in terms of the difference mechanically, but I don't think I've seen discussion on the actual results in the beverage, pp vs fp.
I.E. which could make a better drink if all the settings were configured by an expert on each machine and the roast used, Slayer or Strada EP.

The general impression I get from reading is that pressure profiling was over-hyped and flow-profiling (customized preinfusion) is really where its at, but I don't know if I just succumbed to slayer marketing or not.

I wasn't convinced of pressure profiling worth the work. Albeit I might add line level "post" infusion at the end....

A vibe pump, the right sensors and a micro-controller doing fast PWM is a good way to get automated, flexible pre-infusion, pressure profiling and/or flow profiling (my preference). Easy enough that I'd be interested in why anyone would use a different approach.

On a vibe pump, a simple dimmer and a pressure gauge is a good manual solution; but it would get messy if you tried to automate it.

It's not all that hard to implement a manual pressure profiling system. I did it by replacing the rotary pump on my GS/3 with a variable speed gear pump. The manual control system is relatively simple to build -- basically it's a 24V power supply, a 5V voltage regulator (or a voltage divider made from resistors) and a potentiometer. Mine is a bit more complicated because I added three fixed switched speeds (free flow, high speed free flow and profiling max) and a touch-sensitive knob to switch into profiling mode (actually, so I wouldn't forget to switch out of profiling mode.)

Most of the complexity in building the kind of pressure profiling system being discussed comes from making it programmable. For that you need the above plus an electronic pressure transducer and a microprocessor. You can go even further and install sensors and relays inside the machine to allow the microprocessor to begin and end the shot, perhaps in conjunction with a Bluetooth scale.

I was heading down this road, and actually have the electronic circuitry designed and partly built, but I'm probably not going to follow through with it. Why? After a lot of experimentation, my feeling was that it's fairly easy to manually reproduce a profile and being able to store, retrieve and execute profiles isn't worth the effort.

But even more important, my conclusion was that pressure profiling doesn't provide all that much benefit taste-wise. Varying the ramp up speed made minimal difference. A gradual ramp-down took the edge off light roasts, but the effect was subtle. I did this for a while but eventually gave up on it.

When I learned about Slayer's flow profiling, I decided to add a similar capability to my GS/3. I started by replacing my cheap pressure regulator with a very stable Swagelok model. This allowed me to reduce the line pressure to about 1.5 BAR. By setting the gear pump variable speed motor control to zero, I can get a long, slow pre-infusion, similar to what you can do with the Slayer needle valve. It's not variable like a needle valve, but I found that once I could get the preinfusion time up to about 10 seconds or so, I could grind very, very fine without choking the machine. Generally, I can grind four or more steps finer on my K10.

This technique does help quite a bit with light roasts, but even with grinding finer and running shots as along as 90 seconds (including preinfusion), the sour edge still remained on light roasts. I think what happened is that I hit the point of diminishing returns -- i.e., as you grind finer and finer you reach a point where the extraction yield begins to drop.

This forced me to take a long look at how I was pulling espresso and I realized that I had mechanically been pulling Ristretto practically from my first shots 7 years ago. That worked well back then, but roasts have gotten a lot lighter since. I decided to try pulling longer shots and, lo and behold, my shots started tasting a lot more balanced. They were a bit thinner and weaker, but they were no longer tasting like lemon juice. A good trade off in my opinion.

Another thing I've done is to buy less coffee from ultra-light roaster and more coffee from roasters who are willing to go a tad darker, like medium light or medium. With those coffees I can pull Normale or in some cases Ristretto. When I pull these coffees, I don't do any profiling at all.

We've been jumping through a lot of hoops to compensate for coffee that's been roasted too darned light!