We use a steam mop on my mother-in-law's linoleum, and it seems to do a fairly good job, but I don't know how it would work on epoxy. It may be a matter of getting down with elbow grease and going at it with some pressure to get into those grooves. Epoxy is one of the most resilient and non-staining grouts you can have, so you have a good foundation with which to work. You might check with Laticrete's customer service department to see if they have any options for you, one of the most advanced flooring and grout companies in the industry right now. If anyone had special, high-tech grout cleaning formulations, they probably would. However, I would just try sponging it with some pressure by hand first and seeing what that might do.

Steam damages epoxy grout. You need and old fashioned string mop. That absorb water down in the hollows.

Janitor supply places sell a grout cleaning brush + long handle. Use one of these to scrub or put a piece of towel over brush and mop the grout with it. With the long handle you can stand up to clean the grout. Works great.

I use a steam mop on tile floors, and love it. however, it does not really do anything for the grout...

Ironically I just cleaned all of my tile and grout today in preparation for an appraisal and I have found that the very best way to do it is to use a Magic Eraser sponge! It does require being on your hands and knees but it is super fast and you don't have to apply a lot of pressure- and no product is needed- just water and the eraser. I have found eraser sponges that are better than Mr. Clean on Amazon, and for much less- the ones I have are from the company www.honest-f.com and they last a lot longer and don't disintegrate until the bitter end. This truly is the best way to clean grout (and tile) and I have tried a ton of different methods, as I hate dirty grout! I do have a steam cleaner too and it does nothing to my grout. The eraser cleans the tiles themselves really well, too- not that you want to do this regularly, though, it is not a fun way to clean your floors, but when you need to really, really get it all clean, this is the way to go!