Fine-gauge machines were manufactured and released to the market later in the game and therefore only a limited number of models were available. But not many of those models were manufactured so it is hard to find these machines and they are very sought after.
Below is a handful of fine-gauge knitting machines produced by different companies.
Brother 120, 3.5 mm, 8-pushbutton
Passap E8000, 3.25 mm gauge, electronic
Studio F270, 3.6 mm
Studio F370, 3.6 mm, punch card
Studio SK830, 3.6 mm, electronic