Liquidol was formulated to essentially duplicate the image characteristics of Kodak Dektol, which is a neutral tone developer.
If you want cooler tones than a standard developer such as Dektol, Moersch is really the only option. However even with the Moersch products below, note that the biggest differences in image colour happen on warm tone papers, with neutral papers showing less change, and cold tone papers the least.
SE3 will be subtly cooler than Dektol, Liquidol etc, but may or may not have an effect on Ilford Cooltone paper
SE6 has a significantly stronger cooling effect tending toward blue-black, but again may or may not have a pronounced effect on Ilford Cooltone paper
Finisher Blue (Moersch) is a PMT-based additive which you can add to any developer in incremental amounts to get cooling effects ranging from subtle all the way to blue-black shifts depending on how much you add. You can add it to Liquidol or any other general purpose developer.
SE6 and/or Finisher Blue are really the only products that are likely to have any appreciable effect on a paper such as Ilford Cooltone which is already a cold tone paper. Light selenium toning can potentially help slightly. If none of that makes the paper blue-black enough for you, you're left with gold toning, but even that will tend to have stronger effects on warm papers than cold papers.