Can two sessions of opatch, same database, run at once?

Hi, DBAs

This is 11.2.0.2 RAC on rhel5 x86_64.  I have two rolling-installable patches I need to apply to several databases.  To avoid stopping and starting the same instance more than once, can two sessions of opatch run at the same time?

I mean these sequence of steps:

1.  Stop instance 1

2.  Start opatch for patch A and complete it on instance 1

3.  Start opatch for patch B and complete it on instance 1

4.  Start instance 1

5.  Run steps 1 - 4 for the remaining instances until each patch has been applied in full.

If this works, is there a restriction about which host starts opatch?  Can both opatch sessions run from host 1?