Is there a way I can contribute to the project?
'Contribuire' = kon-tri-bwee-REH. Stress the third syllable.
Use this when you feel underutilised or want to take on more responsibility. It shows proactivity without overstepping. It is especially effective during quieter periods when no task has been assigned.
'C'è un modo in cui' (is there a way in which) is a polite, indirect way to offer yourself for a task. It gives the supervisor an easy out if they say no, which maintains a comfortable dynamic.
Posso dare una mano con qualcosa?
Can I lend a hand with something?
Very informal; use with colleagues, not supervisors
Se ha bisogno di supporto, sono disponibile.
If you need support, I am available.
Formal and open-ended; puts the ball in the supervisor's court
Vorrei essere più coinvolto/a nel progetto.
I would like to be more involved in the project.
More assertive; use after building some rapport
Showing initiative ('iniziativa') is culturally appreciated but must be balanced with respect for hierarchy. Offer help; do not assume permission to act independently on major tasks without explicit approval from your supervisor.