I think it depends whether the cable is buried or not.

Regulation 543.6.1 says:

543.6.1  Where overcurrent protective devices are used for fault protection, the protective conductor shall be incorporated in the same wiring system as the live conductors or in their immediate proximity.

So provided the external cpc is in its immediate vicinity, it could be OK to provide a reinforcing cpc.

BUT Regulation 522.8.10 could be said to imply that if the cable is buried directly in the ground, the armour needs to be able to act as a cpc ... and that would also potentially imply an internal "additional cpc" is also out. Depending on how you view Regulation. 522.8.10 may also be interpreted that a suitable duct (for example, high impact resistance"twinwall" or similar) is able to provide mechanical protection for buried cables, so if using that you can ignore the fact the armour has to be a cpc.

BUT THEN AGAIN, nothing to say any cpc has to be able to take all the fault current, and can't be re-inforced by additional parallel conductors.

If you are using the reinforcing cpc method, the earth fault loop impedance of the combined line conductor and cpc are calculated in accordance with PD IEC/TR 50480. This is referenced from Appendix 4 to BS 7671, and further guidance can be found in the IET Electrical Installation Design Guide.

gkenyon said:

BUT Regulation 522.8.10 could be said to imply that if the cable is buried directly in the ground, the armour needs to be able to act as a cpc

The interesting phrase is, "suitable for use as a protective conductor". That might be read as excluding any cable whose armour is insufficient as a CPC, in which case a conduit or duct would be required and of course the extra CPC would be within the same duct.

I don't think that 543.6.1 is particularly relevant because "wiring system" as defined includes, "parts which secure and, if necessary, enclose the cable" so fastening the extra CPC under the same cleats or cable ties, etc. would include it in the same wiring system.

gkenyon said:

BUT Regulation 522.8.10 could be said to imply that if the cable is buried directly in the ground, the armour needs to be able to act as a cpc

The interesting phrase is, "suitable for use as a protective conductor". That might be read as excluding any cable whose armour is insufficient as a CPC, in which case a conduit or duct would be required and of course the extra CPC would be within the same duct.

I don't think that 543.6.1 is particularly relevant because "wiring system" as defined includes, "parts which secure and, if necessary, enclose the cable" so fastening the extra CPC under the same cleats or cable ties, etc. would include it in the same wiring system.