I know there are rotary machines, designed specifically for tile and grout cleaning, imported and sold by the usual distributors, ie, Alltec, Hydramaster and probably Prochem and others, as they were originally designed for t/m use, but the newer ones are suitable for portable use.
There is even a new Ninja recently launched in the US with 1200 psi and tooled up for hard surface cleaning
Personally, I've had excellent results from a powerwash, which is currently for sale, as I'm starting to listen to my cardiologist !
robbie