Should you wait to switch to the ground frequency until after crossing a runway?
Remember that active runways are always the jurisdiction of the local (tower) controller. Even if a ground controller tells you to cross a runway, they have to clear it with the local controller next to them. So generally you switch frequencies when you have finished crossing the runway unless told otherwise.

I can tell you this is exactly how it works in Boise, Idaho where there are the parallels 10/28 L/R.

However, if you are unsure of any instructions a controller gives you, the basic rule is: ask. The tower controller won't mind, and will typically appreciate the clarification. Just read back the crossing instruction as normal, then ask.


  Right on E, cross 27 R, contact ground .9, N12345, and should I contact ground on the other side of 27R or immediately?