Does anyone make an ASA 1600 or 3200 color film?

Kodak produced a Royal Gold and Ektar at 1000 ISO and there is a Fuji Superia 1600 available on Amazon.

But they are quite rare - if we take a look at the microscope images of photographic film (which also has some notes on how film is constructed) you'll see that the TMAX 400 film is already starting to run low on space for more crystals and it's monochrome. An ISO 800 film has to be more densely packed and requires larger crystals. For a colour process you would need to have space between the crystals in the upper layers for light to pass through the colour filters, it becomes a difficult process and the grain becomes more prominent the higher up the scale you go.

Even the films that did dominate that space are dying out. Eliminating the gaps between the photosites/crystals is inherently taken care of in the process of creating digital sensors. As a result we already see excellent performance at ISO 1600 and beyond from high-end digital cameras.

Just comparing the gaps between crystals in TMAX 400 against the 3.8µm pixel size of a Nikon D3200 (Source: chipworks) you can soon see that digital sensors have a significant edge which does not bode well for the more niche films.

I've shot Fuji 800 pushed two stops and it was fine by me. You lose a little contrast but if you're scanning you can fix that up in post.