A simple tuner might be just a capacitor and an inductor:

^{simulate this circuit – Schematic created using CircuitLab}

For more flexibility, many tuners add a 2nd capacitor to make a pi network:

^{simulate this circuit}

If you were to have two such tuners:

^{simulate this circuit}

Well, now you just have more elements which can be adjusted. There's nothing inherently wrong here. In fact it gives you additional tuning range.

Internal tuners usually do not have much range, and it's likely with an external tuner you won't even need the internal tuner. You might consider simply disabling the internal tuner. Or if your external tuner is manual, you could adjust it for a good match at the middle of the band, then enable the internal tuner to compensate for the slight mismatch as you move within the band. If the external tuner is automatic, I can't really think of a reason you'd need both.

A simple tuner might be just a capacitor and an inductor:

^{simulate this circuit – Schematic created using CircuitLab}

For more flexibility, many tuners add a 2nd capacitor to make a pi network:

^{simulate this circuit}

If you were to have two such tuners:

^{simulate this circuit}

Well, now you just have more elements which can be adjusted. There's nothing inherently wrong here. In fact it gives you additional tuning range.

Internal tuners usually do not have much range, and it's likely with an external tuner you won't even need the internal tuner. You might consider simply disabling the internal tuner. Or if your external tuner is manual, you could adjust it for a good match at the middle of the band, then enable the internal tuner to compensate for the slight mismatch as you move within the band. If the external tuner is automatic, I can't really think of a reason you'd need both.

Another possibility given your situation: skip the external tuner, and instead just pick some fixed component(s) to make a matching network. It's cheaper than buying an adjustable tuner if you don't already have one, in fact you can probably build it from scrap you already have. And you can then mount it outside at the antenna feedpoint to reduce feedline losses.