Ink that cleans?

I like pigmented inks, the downside is that a more strict pen cleaning routine is needed. After using a whole fill of pigmented ink, and flushing of course, I usually like to put a “cleaning ink” on my Pilot Custom 823, given that I can only flush it, and write with that ink for a while.

What I mean by “cleaning ink” is a regular dye ink that will kind of “dissolve” any pigment residue. I will fill the pen up with a Sailor ink for example, maybe a blue or another gentle color(never pink or brown) and just use it until empty, given that Sailor inks are so nicely behaved in my experience, and that the don’t stain cartridges or the bodies of demonstrator pens.

Do you have a recommended ink for this?

For some it might be a bit OCD, but pigment in does stick to pen surfaces and nibs pretty stubbornly, and if there is non-pigmented ink that helps a bit it is always great.

Thank you!