You mean a
"Transport Permit To Carry Firearms for Gun Club Members"? (TP)
Yes, a single TP can apply to multiple firing ranges.
Some smartypants owners even try to list ranges all over the country.
As for transporting a weapon via commuter train... hmmm.
The language of the permit goes thus:
3. While en route to the range from the residence and vice-versa, all firearms must be unloaded. The ammunition and firearm must be secured in two separate cases/boxes and further kept in two separate places (the trunk compartment and the glove compartment)
On the MRT or other commuter train...
You can try to fool yourself that carrying the stuff in separate trolley-like, wheeled-luggage-type bags constitutes 'separate compartments' that are distinct from on-body carry devices (I mean like, what's the legal diff between keeping the stuff in a worn backpack and holstered carry, which --loaded or unloaded-- requires a PTCFOR?)... but to me it seems a really bad idea, security- and safety-wise, before you even get to legal aspects.
Grit your teeth. Bear the traffic.
Use the car.
A TP is valid for three (3) months.