Plasma profiles across the separatrix and scrape-off layer (SOL) in Alcator C-Mod are examined for a range of plasma densities, currents and magnetic fields in Ohmic L-mode discharges and for a subset of conditions in Ohmic H-mode discharges. In all plasmas, electron pressure gradient scale lengths () exhibit a minimum value just outside the separatrix (i.e. in the near SOL), forming the base of a weak (strong) pedestal in L-mode (H-mode) plasmas. Over a wide range of conditions in Ohmic L-mode discharges, at this location are found to track with a monotonic function of electron collision frequency, when this quantity is normalized according to the framework of electromagnetic fluid drift turbulence (EMFDT) theory. Moreover, at fixed values of normalized collisionality parameter (characterized as the 'diamagnetic parameter', αd), electron pressure gradients in the near SOL increase with plasma current squared, holding the MHD ballooning parameter, αMHD, unchanged. Thus, the state of the near SOL is restricted to a narrow region within this two-parameter phase-space. An implication is that cross-field heat and particle transport are strong functions of these parameters. Indeed, as αd is decreased below ∼0.3, cross-field heat convection increases sharply and competes with parallel heat conduction along open field lines, making high plasma density regions of αMHD–αd space energetically inaccessible. These observations are consistent with the idea that the operational space of the edge plasma, including boundaries associated with the tokamak density limit, is controlled by EMFDT.