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.
Ultrafine gauge
Studio SA10, 2.8 mm
Fine gauge
Brother
Brother KH110, 3.6 mm, 8-pushbutton
Brother KH111, 3.6 mm, 8-pushbutton
Brother KH120, 3.6 mm, 8-pushbutton
Brother KH131-48, 3.5 mm, intarsia only, basic/manual
Brother KH1101, 12-stitch punchcards
Corona
Corona 3.5, 3.5 mm, basic/manual
Empisal
MAYBE: Empisal Instant Knitter, manual/basic
Passap
Passap E8000, 3.00 mm gauge, electronic
Silver Reed
Silver Reed SK370, 3.6 mm, punchcards
Silver Reed SK570, 3.6 mm, punchcards
Silver Reed SK570, 3.6 mm, electronic
Silver Reed SK830, 3.6 mm, electronic
Studio
Studio F270, 3.6 mm, punchcard
Studio F370, 3.6 mm, punchcard
Studio 830, 3.6 mm