From the description it already has an underlayment attached.But it might depend on what you are laying it over top of.

So by adding more underlayment is not going to help improve the comfort and noise level then?

The Coretec Plus with the attached underlayment is NOT ALLOWED to have more added. Sigh. This is the BIGGEST downfall of vinyl.

Most vinyls (some of the Coretec are included in this list) do NOT allow underlayment (underpadding) - period. If you want underpad for acoustic or thermal insulation you need to work with laminate.

There are VERY FEW vinyl products that allow underpad. Those products list the option in the installation instructions with wording to the effect of:

"Underlayment specifically designed for LVP to a maximum thickness of 1.2mm"

And the only thing that comes in that thickness = mass-loaded vinyl underlayment specifically designed for vinyl plank flooring (can be as much as $2/sf).

An even SMALLER amount of vinyl products (usually the very thick ones that are rigid and do NOT have underlayment attached...which means your choice is 'out') will allow cork underlayment to a MAXIMUM of 3mm thick.

The ORIGINAL Coretec product (NO cork underlayment attached) allows 3mm cork. EZ Lay vinyl and Drop N Done vinyl ALSO allow cork (they allow a maximum of 4mm of cork). These are some of the ONLY products that allow cork as underlayment.

Everything else must sit on something like plywood, concrete, etc. If you must have more acoustic insulation you may need to work with a water proof laminate like Aquaguard. This product allows 6mm or even 12mm of cork underlayment without issue.

I'm guessing that the thickness and strength of some products does not allow to add underlayment that might overstress the edge joining system. Excess flex on a thinner product would probably cause the joints to uncouple. Stick with the manufacturer's recommendations. Also, adding more underlayment doesn't make the floor quieter. It might transmit less noise below, but that only pertains to a multi-story building.