Why diversification rates vary so extensively across the tree of life remains an important yet unresolved issue in biology. Two prominent and potentially independent factors proposed to explain these trends reflect the capacity of lineages to expand into new areas of (i) geographical or (ii) ecological space. Here, we present the first global assessment of how diversification rates vary as a consequence of geographical and ecological expansion, studying these trends among 15 speciose passerine families (together approximately 750 species) using phylogenetic path analysis. We find that relative slowdowns in diversification rates characterize families that have accumulated large numbers of co-occurring species (at the 1° scale) within restricted geographical areas. Conversely, more constant diversification through time is prevalent among families in which species show limited range overlap. Relative co-occurrence is itself also a strong predictor of ecological divergence (here approximated by morphological divergence among species); however, once the relationship between co-occurrence and diversification rates have been accounted for, increased ecological divergence is an additional explanatory factor accounting for why some lineages continue to diversify towards the present. We conclude that opportunities for prolonged diversification are predominantly determined by continued geographical range expansion and to a lesser degree by ecological divergence among lineages.