Some songs are in the key of F so trying to fill in or accompany the singer on a key of C harmonica is nearly impossible. I have a chromatic harmonica in the key of F but it"s only a 12 hole so doesn't go high enough on the notes.
At the time of writing:
- Suzuki offers it's 12 hole chromatic harmonicas in various keys (including F), but not it's 14 or 16 holes. See: https://www.suzukimusic.co.uk/products/harmonica/chromatics.html
- The same is true of Seydel, only some of it's 12 hole chromatics come in other keys than C: https://www.seydel1847.de/chromatics.
- The same is true of Hohner, only some of it's 12 hole chromatics come in other keys than C: https://www.hohner.de/en/instruments/harmonicas/chromatic
- As far as I can tell,the same is true of Eastop.
However some of those companies will allow you to order custom-made harmonicas (at a much higher cost, obviously). I know at least Seydel and Hohner do this, so possibly you could ask them for a 16 hole chromatic in F.
Having said that, it's worth noting that the vast majority of Chromatic players just use a harmonica in C (one exception being Irish music players, who tend to use chromatics in D or G).
Playing in the key of F on a Chromatic in C is fairly trivial - you only need to use the slider when playing the Bb (which you will find on holes -2, 3, 7 and 11 draw with the slider in).