There are multiple references to touch and go operations with fuel in the external tanks. Check your Normal procedures section for guidance.
Some places it says to land "with little, if any, usable fuel in the external tanks" and other places it says "Crossfeed from... external tanks may be done during… touch and go landings"
Not really a yes it is OK or a NO it is NOT OK, to do touch and goes with external tank fuel and crossfeed operations but your sink rate is limited to 300 FPM at touchdown any time there is more than 500LBS in the external tank. Less than 500 LBS is considered empty and the tank should not be used for crossfeed as pressure will probably not be maintained as the fuel level is too low to maintain pump pick up with the changing pitch angles.
Do you have fuselage tanks installed? If so you cannot have usable fuel in the external tanks with the fuselage tank not full (20,000LBS+)