I have a La Pavoni machine that was made in 2001 and looks to be all "Millennium" parts with the exception of the group. It's one of the machines that has the black base. If I had a Millennium Europiccola machine that had the updated group and a chrome could I pull the millennium group off the Europiccola and swap it out with the Pro? Could I also take the Chrome base of the Europiccola and swap it out with the black base of the pro? It seems like the bases are the same size from what I've read, but wasn't sure.

The replacement base at espressocare says it is applicable to all models. Looks like your 2 bases are interchangeable.

+1 about swapping bases. You may need to swap the base and subbase together, because the subbase attachment changed a few times over the past 40 years or so. A really old Europiccola base (pre '78 or so) may not swap well because of the different switch cutout.

And to address your other question about swapping groups -- Yes you can swap over a complete grouphead assembly between Gen 2 pre-millennium, and Gen 3 millennium machines including the Europiccola, Pro, Romantica, even Gaggia Factory. Of course the portafilter and baskets need to be swapped so as to stay with their proper grouphead.