The Forge should let you make ST items. The why is simple: ST items although not necessarily rarer than UTs are often more in demand than UTs. I mean, I like to get a Ogmur like anyone. But I don’t need one to play Knight, and am not especially expecting one or looking for one. I will take advantage of one when I next get one. But ST items I much more likely to be explicitly looking for one, as I have a partial set and want to complete it. In fact I am looking for a number of such. Off the top of my head I need the following items to complete a set:
- Embellished Quiver from Ruins
Wraith’s Brigandine from Lib- Imperial Keepsake from Reef
- Theurgy Wand from Janus
- Mercy’s Bane from O2
- Memento Mori from Ghost King
- Pernicious Peridot from Pit
- Staff of Eruption from Shaitan
- Carved Golem Remains from Halls
- Magic Wand from Encore
- Daybreak Chakram from Thicket
- Kamishimo from MT
- Honeytomb Snare from Nest
All of those I have the other three items; there are other sets I have two or even one item of i might like to complete someday but am not actively looking for. Some of them I have little hope of getting as I do the dungeons so rarely. Other dungeons/quests I do pretty often but am at the mercy of RNG. Until I get the set I am reluctant to use it, and potentially lose it before completing.
As for how, I would make some changes to the Forging process. As well as raw materials it would depend on you having other ST items, mostly from the set. This would stop people just making a whole set out of surplus UTs.
You might e.g. need to have two or three of the set before forging items from it. You might have to use one or more items from the set as raw ingredients – this makes sense for the many sets where one item is far more common than others; the ring from the Swarming Huntress Set for example. Or ST items might need another sort of Ore, which you only get from other STs. Or some combination of these; it can use the same mechanics as UT forging but the pool of items can be different, even completely distinct.