Transformers trained on huge text corpora exhibit a remarkable set of capabilities. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities, potentially yielding a combinatorial explosion of what operations it can perform on an input. Motivated by the above, we aim to assess in this paper "how capable can a transformer become?". In this work, we train Transformer models on a data-generating process that involves compositions of a set of well-defined monolithic capabilities and show that: (1) Transformers generalize to exponentially or even combinatorially many functions not seen in the training data; (2) Transformers that generate the intermediate outputs of the composition are more effective at generalizing to unseen compositions; (3) The training data has a significant impact on the model's ability to compose functions (4) Attention layers in the latter half of the model seem critical to compositionality.