CM Chokes Rating

Just a simple question, if I've got a cm choke rated for 10amps at 300v there would be no problems using it for, let's say, 40amps at 24v?
Or there are some saturation mechanisms behind that I'm missing?
If one were to pay some attention it is immediately evident that the dot polarity (coupling) used in CM chokes is meant to obtain a 4x inductance for CM signals and nearly zero inductance (passthrough) for DM ones.

CM chokes thus have almost zero flux in their cores, and are therefore unlikely to saturate with increasing DM current. But the resulting rise in temperature (due to resistance) could be an issue.

The voltage rating is only an indicator of insulation strength, and so 24V is perfectly OK.
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