Third width cabs (not half cabs) in the R62/62A were converted to full width cabs - that is how the existing full width cabs were created for those cars. As such the full width cabs can be converted back to third width.
All newer cars (R44 (now retired), R46, R142, R142A, R143, R160, R188 and the soon to come R179 and R211) all have full width cabs but only in the "A" (operating) cars. All the other cars (B and C units) have no cabs.
R68 cars were built with a full width cab at one end and a third width cab (with full controls) at the other. Each car can be the operating car as consists are changed especially if a car has to be taken out for maintenace.