Sadly only one aircraft will bind with the controller at a time.  I can bind the P4 controller to the P3P aircraft but switching to the P4 aircraft is not possible without rebinding.    The selector at the opening of the Go App does not work once the Tx is powered on, it defaults to the last aircraft bound to the Tx.  Doing a rebind will switch the app display to the correct configuration of the newly bound aircraft.  ie turn on app with P4 display, bind to P3P and the display & commands change to P3P and vice versa.
My FrSky Tx would bind to any number of receivers once it powered up and I selected which model I wanted to use.  Go App should work like this too.
(All hardware is loaded with the lates firmware versions)

The Yuneec controllers do this, 1 remote for all.
Come on DJI, you guys should be able to do this also!!

I'm not sure what you are trying to accomplish. Your P3 remote will bind to your P3 and P4. And your P4 remote will bind to the P4 as weel as your P3.
But each time you use the controller for a different aircraft, you have to rebind no matter what.

DJI-Ken Posted at 2016-3-21 16:11
I'm not sure what you are trying to accomplish. Your P3 remote will bind to your P3 and P4. And your ...

Well I have two Txs and one HDMI module.  Also I would just like to go in the field with one Tx for both birds.  I should be able to select which model to control at the opening screen of the app be it a P4, any variation of P3, Inspire or Matrice.  My other RC controllers to this as well as the Yuneec as the previous poster pointed out without having to rebind each time I switch machines.

hummingbird.uav Posted at 2016-3-22 06:20
Well I have two Txs and one HDMI module.  Also I would just like to go in the field with one Tx fo ...

Binding literally takes less than 10 seconds. That's as good as it's going to get.Under RC settings, there's a "Linking RC" button. That should link you to different aircraft.

I found a unit that can bind/control with nearly any drone, even while you are flying it... ;-)
A company called Battelle, produces an instrument called DroneDefender.
http://www.battelle.org/
Here's a demo:

I hope these don't ever find their way up here...

RedHotPoker

DJI-Ken Posted at 2016-3-21 18:36
Binding literally takes less than 10 seconds. That's as good as it's going to get.Under RC settings ...

Thanks Ken that's probably what I'll be doing when I want to use the HDMI output on the P3.

RedHotPoker Posted at 2016-3-21 18:45
I found a unit that can bind/control with nearly any drone, even while you are flying it... ;-)
A co ...

  Drone hijacker. That's a really scary device!