I cover this at some length in my book, "Thermodynamic and Transport Properties of Fluids." The Ebook is free on these days: 4/16,4/24,5/2 at this link https://www.amazon.com/dp/B07Q5L1CHT The software is always free at this link http://dudleybenton.altervista.org/software/index.html and one of the Excel AddIns (also free) may be helpful.
We know theoretically how pressure and density must interact at the critical point. Specifically, the first two partials (dP/drho and d²P/drho²) must be zero at the critical point for it to exist. This is mathematically equivalent to having three roots at the critical point. Simple equations of state (e.g., van der Waals) can reproduce this behavior, but may not fit data well anywhere else. In fact, the critical compressibility for a van der Waals fluid is Zc=3/8, which is larger than any known substance. The liquid densities are also off by a factor of 1/3 to 1/2 for the van der Waals EoS, as are the saturation pressures. What this means is that, in order to be accurate in all of these details, quite complex approximations are necessary. For example, see the properties of steam (1967, 1969, 1984, 1995, 1997, and 2020). This can require a lot of work, a lot of data, and a lot of software. Bringing all this together for any single substance is difficult. Steam is worth the effort because of the many industrial applications. It may not be worth the effort for other less-used fluids. You can get good and accurate properties for many fluids from NIST with their REFPROP software. If they don't have what you need, I'd be glad to pull the properties together for you. I've done it so many times, it isn't hard for me and I have all the software ready to go. I recently did this for NOVEC-649, which has the distinction of the lowest greenhouse potential of any refrigerant. Was there some particular fluid you needed or were you interested theoretically? If your interest is theoretical, steam is an excellent example. For example, there's lots of data, but most of it is clustered. This naturally arises from the experimental apparatus used to acquire the data.