McGrath, in the 20's the Gibson Company produced the "Mandolute" which was a single-coursed four string instrument like a mandolin that was tuned like a tenor banjo. CGDA and also higher tunings DAEB. It has a mandolin sound in register but not in quality as the mandolin characteristic is defined by the double-strung strings.

My friend Bill Rutan has had one made which he uses for gigs. It can play all the chords that are needed as on a uke but is open-voiced like a tenor banjo.

Everyone:
Both the tenor banjo and the uke are more harmonically versatile than for which they are given credit. You can play sophisticated jazz tunes on both. Chord melody is facilitated by the use of just four strings. An alternate tuning would be CGBD as used on a plectrum banjo but for the uke, it might have to be tuned higher. The fourth string would be thicker like on a baritone uke unless you raised the C an octave. This could be done on a tenor banjo tuning as well (often called a "high C" tuning).