Rejoin SID
 

This may be difficult to explain but here goes...

If a SID does not prescribe a specific track to intercept a radial can the pilot choose the track to intercept that radial?

If he can choose, can the delivery controller give an additional clearance that includes the track to be used for intercepting the radial? And will the pilot after interception rejoin the rest of the SID?

A bit confused. Have you been taken off the SID by ATC? If so you should be either vectored to intercept or maintain current heading to intercept. Otherwise the SID should explain exactly the tracking requirements e.g Runway heading to 1500", right 030 to intercept the 045 radial etc. The ACD won't assign extra parts to a SID, it IS the clearance.

Standard intercept is 30 degrees off the radial or track to fix unless otherwise specified in the procedure.