Would it make sense and be safe to put power conditioner in front of PS Audio regenerator?

Not in front of–but you could try beside. Use one for the source, the other for the amps. Use same twin outlet. Also try direct to the receptacle with no conditioners. 

This brings up a thought after reading the post.

I assume the output of the PS Audio regenerator is wired as a grounded AC power system. Therein NOT left floating. Floating...Therein two Hot ungrounded conductors with no reference to ground.

If the AC output is a grounded AC power system (which I hope it is) and not all audio equipment that, is connected together by wire interconnects, is fed from the regenerator, like say a power amp that is plugged directly into the wall out, are the two 120V power sources in phase with one another? 

Simple test. Use a multimeter, (set meter on AC volts auto scale, or above 250Vac scale). Measure from a receptacle HOT contact (small slot) on the regenerator, to the HOT contact of the other receptacle of the wall duplex receptacle the regenerator is plugged into.   

If the two 120Vac sources are in phase with one another you will measure zero Vac nominal. If the two 120Vac sources are out of phase with one another you will measure 240Vac nominal. 

.

Just checked the Premier. The input voltage it shows is 119 and the output voltage is 121. Why does it increase the voltage when 119 volts is perfectly fine ? You can't adjust the output voltage, or frequency.

Do you think that newer PS Audio P5 would be significantly better ? I could also experiment more with power cords from the wall but this Purist works well, I did compare it to a few others.

"I could also experiment more with power cords from the wall but this Purist works well,"

Unnecessary audionervosa.

I use a PPP. It's 18 years old. PS Audio refreshed it in 2020, and good for another  10 years. They no longer support it.

The output display ISN'T 100% accurate depending on the calibration of the output/ display. There's  an adjustment pot underneath  the unit to fine tune it, which is done at the factory to display 120V.

With a Google  search and  a MM it can be done, if you're  a tinkerer. If you don't have experience with live circuit boards, best to just leave it be.

"Do you think that newer PS Audio P5 would be significantly better ?"

P5 is 2 generations old. Long discontinued. A newer PP isn't  going to magically transform  your system. If anything the psychological  "new box" will be in play for a hot minute. Naturally, just my take on using a PP.

I am not going to replace the Premier for as long as it works properly. Yes, I heard it is no longer serviced by PS Audio.

I wouldn't exactly expect dramatic improvement from the newer regenerators, significant improvents perhaps.

But the wall current is not going to improve, I guess, anyway.

@jea48 Not saying I don't recommend a dedicated line if you can.  I have one, 10 awg.  

But the dirty power happens outside the home and you can't do anything about it with a dedicated line.   Not most of the dirty power, but 100% of it so long as you have nothing else on the circuit.

I discussed getting other loads off your audio power circuit.  

Jerry