I’m not sure which versions of Steinberger instruments / hardware you’re looking at, there were a number. I don’t have actual Steinberger or Spirit instruments on hand. I
do have a Hohner 6 string with a trem bridge and a bass that started out as an 80s Cort headless, both with “Licensed by Steinberger” hardware so feel free to take this with most of a shaker of salt.
The bass bridge is wider than the guitar bridge and both are recessed into the body. Call it 3 3/16” for the guitar and 3 5/8” for the bass so the bridge recess on the body would need to be enlarged for the 4 string bridge.
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Also, the bass neck is slightly wider so while the bass headpiece may screw into the guitar neck it will overhang and the string spacing may be off.
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You aren’t going to find double ball end strings the right length also but an adapter can be made or purchased, see the picture of the guitar neck. Also, the newer Spirits and Steinbergers may, probably do, use something different so they don’t need double ball end strings so the last part may be a moot point.
Definitely check these measurements against newer hardware but I’d say it’s doable but may require some routing and finish touchups.
Another option if the bass string ball ends fit in the guitar claws would be to get some spacers made up so you can use 4 guitar saddles and the existing bridge/tuner. You’ll still have to figure out something at the neck end.