The Cloyne harp has a number of points that demonstrate that it did not use the normal Gaelic harp tuning scheme as recorded from the old harpers by Edward Bunting in the 1790s.
There is a short row of seven extra strings in the mid-range, and the unusually large number of 45 pins in the main row. There is also a kink in the harmonic curve at pin 37 (9 from the bass).
Suggestions that the seven extra pins are to provide a parallel rank of seven extra strings in the mid-range can be disproved on inspection of the Cloyne neck; viewed from the top, the seven extra pins project no further on the left hand side than the main rank does, so any strings attached to those extra pins could not fall as a second, parallel rank, but must be considered part of the main rank, falling between the other pins.
Mike Billinge suggested that this single combined rank of strings could split into two on the soundboard, allowing a chromatic stringing like an Arpa Doppia. The extra density of strings in the mid range would allow three ranks for the crossover between left and right hand.
Because we only have the neck and pillar of the Cloyne harp, any reconstruction of the string geometry and soundboard layout is pure speculation.
Note that such an arpa doppia style arrangement has to be set up either for a left-hand-treble player, or for a right-hand-treble player: unlike diatonic Gaelic harps, the instrument is not playable both ways round. Also note that the seven extra strings should probably pass over the lower rank pins as bridge pins, allowing them to be positioned one note higher or lower on the instrument.