Three Conductor Cable Plus One Single Conductor Cable for Three Phase-Four Wire.

Depends on the definition of OK, I'd say.

And what the customer says, assuming you were going to ask him for a deviation.

Is it allowed anywhere? I'd do it back on the farm in Ark.

I wouldn't allow it in anything I could be held accountable for if somebody were to lick the conductors.

Check the local codes, if any. Maybe you can use the conduit, itself, and save wire.

If there is an imbalance such that the neutral carries significant current, and if the neutral and the 3C cable enter a metal enclosure separately; then there could be inductive heating of the enclosure.

I consider to pull same size of single conductor cable for neural phase same as main phase. In the case of magnetic flux causing heating, single conductor may be provided with brass armour or with non-metalic gland plates. I am not sure if cable clamp is to securely fix three conductor cable and single conductor cables.

Is it non-metallic or non-ferrous gland plate or gland plate with a groove cut to prevent circulation of eddy current.?.

Yes. That's why I intended.

Be specific.

How would you're client / employer view your mistake? Not quite as badly as finding out you have tried to cover it up with a potentially dangerous remedy.

If you were going to the trouble of pulling an earth conductor you might as well use the 3 phase cable to pull in a new 4 core cable, this would be the best practice.

My thought exactly! I would also ask about the ground (earth) wire. Decades ago we used the conduit, not legal in most codes since the 60's. (Pretty good that I can still remember that far back. Now, what is my new wife's name?) If the ground is OK, The neutral may be able to be calculated. That is legal in the NEC (American Code). OP does not say what the applicable code is or where he is, and I don't know other codes. If in question, pull 5 new wires.

One of the posters said he would do it back on the farm in Arkansas. Still happens out on the farm, but Arkansas has come into the 20th century, you have to go by NEC 2008 in Arkansas now. -- JHF PS: GA

You need to look at what was specified and for what use.

The 3 phase cables should all be together however if your using the neutral, that should also be in that cable, so, yes replace a 3 conductor cable plus 1 conductor with a 4 conductor cable.

However what is being used for the earth ?
Some people say to use the conduit or Steel wire of the SWA cable, but this can be considered bad practice, and indeed may not be allowed by local codes / electrical bodies.

As a general rule all conductors of the same circuit should be going through the same cable.
And yes, the earth to protect what ever this would be supplying is considered part of the circuit.

There could be many arguments on different ways to do this, but if its all in one cable hopefully there would be less issues.

It is not "best practice". I would pull the wire out and replace it. And yes, it will be expensive. Mistakes usually are. Dangerous? No. Confusing to the next technician who might have to do this work? Very.

That being said, code item 250.134B (exception 1) might be applicable for adding ground wires in new installations as well as existing installations. Permission is granted to run a separate ground wire outside the conduit in accorance with 250.130(c) when installing replacement grounding type receptacles or EXTENDING A NON GROUNDED BRANCH CIRCUIT to a grounding type receptacle when no equipment grounding wire or means is available in the branch circuit.

Presumably if there was room in the conduit, you "could" run itside as well. But this is just MY opinion. I usually find that conduits are too small to play games like this.

The reason I am not sure if this code item applies is your statement that you accidently ran 3 wire instead of 4 wire between two switchboards. Its not a "branch circuit". If I were the inspector I would demand you replace the three wire with proper four wire cable for that reason.