This is very much a personal view, I don't profess it's authoritative.
I don't attempt to pull doubles if I understand correctly here, a double being the addition of a second pull using the same puck. My own relatively short experience is that to optimise the grind, tamp and taste for a pull means that it just gets destroyed to use it again. No different from using a teabag twice or emptying a pot and starting again with the same loose leaf tea. Urghh, I am English after all!
In fact, I pulled a double by default the other day when talking and distracted. I forgot to change the basket, I pulled, it was flat, it looked weak, I added the milk and it would quite easily have made a good medical specimen

. Needless to say, I immediately poured it down the sink. So, my own take on things is that a Pavoni is a low shot-volume set-up, no big deal, just factor it into the routine. If one can't adapt around it then maybe the answer lies in a different machine. Either pull two separate baskets for your shot/capp or make two drinks to give you the volume of 'hit' you're looking for. It's the latter that I follow and which described in an earlier thread precisely because a solitary double out of the Pav is not enough for me either.
When I first got the Pav it felt strange to use a basket that dropped in and out of the portafilter without being held in place and it did not seem popular out there, however I liked it from very early on. So simple to turn upside down and knock out without losing the basket, it doesn't take much effort to get the technique. Now whilst one could redose, distribute and tamp easily enough, I took the advice of the seasoned Pav user I visited and bought a second basket from the beginning, therefore when I start my two-pull routine I've got both barrels ready to fire. It's obviously fast and easy to drop a second ready-prepared basket straight in, lock and go and without touching any hot surface or losing the 'important for some' time in keeping going given the Pav's continuously-heating nature.
I have tried adding both together for a larger shot and I have tried frothing the milk volume together rather than one at a time which does have benefit until you really get good on a Pav. However, and forgive me for this, the size is just too American for me. If I were on the move and prepared it into a flask or take-out cup for the car then no problem but in the home 9oz is as big as I want to drink. Purely personal preference. I kind of like finishing one, looking at the bottom of the cup and savouring and then feeling good as I pick up the second cup that I can do it all over again.