We prove several new congruences for the overcubic partition triples function, using both elementary techniques and the theory of modular forms. These extend the recent list of such congruences given by Nayaka, Dharmendra and Kumar [‘Divisibility properties for overcubic partition triples’, Integers 24 (2024), Article no. a80, 9 pages]. We also generalise overcubic partition triples to overcubic partition k -tuples and prove arithmetic properties for these partitions.