At least some two-plate states suggest that if you're registered in a two-plate state you must display both plates within their borders. And some even suggest you must have two plates even if your state only issues one, though this scenario would probably not withstand federal scrutiny. In Washington,
License plates must be: (i) Attached conspicuously at the front and
rear of each vehicle if two license plates have been issued; (ii)
Attached to the rear of the vehicle if one license plate has been
issued.
If it was issued, you must display it. California law says
(a) When two license plates are issued by the department for use upon
a vehicle, they shall be attached to the vehicle for which they were
issued, one in the front and the other in the rear. (b) When only one
license plate is issued for use upon a vehicle, it shall be attached
to the rear thereof, unless the license plate is issued for use upon a
truck tractor, in which case the license plate shall be displayed in
accordance with Section 4850.5.
So if you were issued one, you can drive with one, and if the department (arguably and statutorily "The Department of Motor Vehicles") issued two, you must display both.
You might think that you could therefore remove one out of state plate when in California, but they also require (as of this year) that
(a) A license plate issued by this state or any other jurisdiction
within or without the United States shall be attached upon receipt and
remain attached during the period of its validity to the vehicle for
which it is issued while being operated within this state or during
the time the vehicle is being held for sale in this state, or until
the time that a vehicle with special or identification plates is no
longer entitled to those plates; and a person shall not operate, and
an owner shall not knowingly permit to be operated, upon any highway,
a vehicle unless the license plate is so attached.
The law in Oregon says
A person commits the offense of failure to display registration plates
if the person operates, on the highways of this state, any vehicle or
camper that has been assigned registration plates by this state and
the registration plates assigned to the vehicle or camper are
displayed in a manner that violates any of the following: (a) The
plate must be displayed on the rear of the vehicle, if only one plate
is required. (b) Plates must be displayed on the front and rear of the
vehicle if two plates are required.
Somehow, they failed to cover the condition that a person does not have plates issued by Oregon. The law in Ohio is that
(1) No person who is the owner or operator of a motor vehicle shall
fail to display in plain view on the front and rear of the motor
vehicle a license plate that bears the distinctive number and
registration mark assigned to the motor vehicle by the director of
public safety, including any county identification sticker and any
validation sticker issued under sections 4503.19 and 4503.191 of the
Revised Code
This doesn't even make an exception for vehicles from some adjacent state which have only one plate. If you otherwise keep your nose clean, the law says
A law enforcement officer shall only issue a ticket, citation, or
summons, or cause the arrest or commence a prosecution, for the
failure to display a license plate in plain view on the front of a
parked motor vehicle if the officer first determines that another
offense has occurred and either places the operator or vehicle owner
under arrest or issues a ticket, citation, or summons to the operator
or vehicle owner for the other offense.
but you can still get busted for driving your car. Finally, Montana says
a person may not operate a motor vehicle, trailer, semitrailer, pole
trailer, or travel trailer upon the public highways of Montana unless
the motor vehicle, trailer, semitrailer, pole trailer, or travel
trailer is properly registered and has the proper license plates
conspicuously displayed... (1-plate exception for motorcycles
etc)...All other motor vehicles must have one license plate displayed
on the front and one license plate displayed on the rear of the motor
vehicle.
One thing to notice is that these laws are in sections on vehicle registration and not operation, where separate sections of the code regarding street-legal vehicles
prohibit driving without lights or a muffler. Under the full faith and credit clause, I think your act of registering a vehicle in PA is given credit in OH, because the requirement pertains to registering, not the conditions for legal operation on the road.
