Originally a Neapolitan song, this famous melody has been adapted into countless solo piano transcriptions. Its enduring popularity stems from its sweeping melodic arch and sentimental character.
The primary challenge is to maintain a singing tone while balancing the melodic line against the accompaniment.
Comparable difficulty and character — good candidates for what to learn next.
'O sole mio is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 5.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of 'O sole mio lasts about 3 minutes.
'O sole mio is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include 'A mugliera ca primm''e spusà!! by Eduardo Di Capua, 'A robba fina! by Eduardo Di Capua, 'A grott'azzurra by Eduardo Di Capua — see the full similar-pieces list on this page.