During embryogenesis, chromatin accessibility profiles control lineage-specific gene expression by modulating transcription, thus impacting multipotent progenitor states and subsequent fate choices. Subsets of cardiac and pharyngeal/head muscles share a common origin in the cardiopharyngeal mesoderm, but the chromatin landscapes that govern multipotent progenitors competence and early fate choices remain largely elusive. Here, we leveraged the simplicity of the chordate model Ciona to profile chromatin accessibility through stereotyped transitions from naive Mesp+ mesoderm to distinct fate-restricted heart and pharyngeal muscle precursors. An FGF-Foxf pathway acts in multipotent progenitors to establish cardiopharyngeal-specific patterns of accessibility, which govern later heart vs. pharyngeal muscle-specific expression profiles, demonstrating extensive spatiotemporal decoupling between early cardiopharyngeal enhancer accessibility and late cell-type-specific activity. We found that multiple cis-regulatory elements, with distinct chromatin accessibility profiles and motif compositions, are required to activate Ebf and Tbx1/10, two key determinants of cardiopharyngeal fate choices. We propose that these 'combined enhancers' foster spatially and temporally accurate fate choices, by increasing the repertoire of regulatory inputs that control gene expression, through either accessibility and/or activity.