Making paint with polyurethane

I have no experience with what you are proposing, but at least before hearing otherwise from someone with specific knowledge about such a system, I would advise against using it for work meant to be permanent. First, it is experimental and as such we do not know if it will fail, either soon after completion, or perhaps down the road. I am guessing that the do not thin with water is due to it already being thinned to allow for the use of a roller and allow for leveling. Any more thinning could make it insubstantial. The same is true of adding dry pigments. They may be underbound as you are essentially making a leaner paint. I for one have not mixed polyurethane with acrylic dispersion paints and don’t know if they are even compatible. I will shoot your question to those more “in the know” about acrylic dispersions. Additionally, I have used water-borne polyurethane coatings on craft projects, and they do yellow rather strongly.
However, as I wrote, this is out of my area of expertise. Let’s see what others have to say. Finally, what are you hoping for with such a mixture? Is it economy of is there an optical or surface effect? Perhaps if this turns out to be a less than desirable paint, experts in aqueous dispersion paints can point you to a more promising medium/mixture.

​The worst paint failure I ever saw involved homemade paint made with water-borne, home improvement store polyurethane varnish as the binder and some sort of powdered colorant (not artist’s pigment) in a simple mixture. The “paint” flaked completely off the substrate (acrylic-primed cotton duck) and so lacked flexibility and adhesive strength that the slightest touch on the underside provoked a crackling sound.

The answer depends upon the type of polyurethane paint you intend to use. Polyurethane paint can be formulated as two-part solventborne, single pack solventborne (oil modified) and water dispersed paint. Since you referred to thinning the paint with water, I will assume you refer to the latter.
Adding acrylic paint with its own additives, i.e., surfactants, thickeners, and defoamers, often do not play well with the additives in polyurethane paint. Additives are specifically chosen and tested for each type of resin, such as acrylics or polyurethanes. In addition, thinning the paint alters its pigment volume concentration and other properties which adversely affect its application, resulting in undesirable performance. This is why manufacturers warn about altering the paint.

​Thanks Matthew and George.

​When creating experimental mixtures like that, failure in the coating is often apparent directly upon drying, in form of permanently cloudy films, drying defects like crazes and bumps, enhanced film sensitivity to ammonia or solvents, etc. Long-term adhesion might be affected also. It is hard to tell without aged samples. Polyurethanes, whether water or solvent-borne, dry to a stiff, if not brittle, coating and since you intend to use paper and canvas for your substrates, polyurethane wouldn’t be suitable in any case. If your aim is to create perfectly smooth, enamel-like paint applications, then an acrylic pouring medium would be a much safer way to go.