39th game would distort the competition, no doubt about it.
Playing a cup-tie abroad though, that makes a lot of sense.
Take the League Cup, let's face it, that is a competition in serious need of a shot in the arm and PL teams enter at a later stage than everyone else anyway.
So how about this - a PL only qualifying round, each team in the Premiership drawn out the hat paired up with one another at a neutral venue, also randomly drawn.
The ten winning sides then go into the draw against 22 league clubs and away you go with the competition proper.
You could even set up one or two of these matches a week early in the season.
Maybe even include "guest teams" from other countries in the draw (The Old Firm would be up for it, I'm sure...)
No-one loses any home games, the format of the league is retained, the PL clubs pocket an extra big tasty wodge of cash. (I'll settle for 10%, as this is my idea.)