We present $sim10-40,mu$m SOFIA-FORCAST images of 14 intermediate-mass protostar candidates as part of the SOFIA Massive (SOMA) Star Formation Survey. We build spectral energy distributions (SEDs), also utilizing archival Spitzer, Herschel and IRAS data. We then fit the SEDs with radiative transfer (RT) models of Zhang & Tan (2018), based on Turbulent Core Accretion theory, to estimate key protostellar properties. With the addition of these intermediate-mass sources, SOMA protostars span luminosities from $sim10^{2}-10^{6}:L_{odot}$, current protostellar masses from $sim0.5-30:M_{odot}$ and ambient clump mass surface densities, $Sigma_{rm cl}$ from $0.1-3:{rm{g:cm}^{-2}}$. A wide range of evolutionary states of the individual protostars and of the protocluster environments are also probed. We have also considered about 50 protostars identified in Infrared Dark Clouds and expected to be at the earliest stages of their evolution. With this global sample, most of the evolutionary stages of high- and intermediate-mass protostars are probed. From the best fitting models, there is no evidence of a threshold value of protocluster clump mass surface density being needed to form protostars up to $sim25:M_odot$. However, to form more massive protostars, there is tentative evidence that $Sigma_{rm{cl}}$ needs to be $gtrsim1:{rm{g,cm}}^{-2}$. We discuss how this is consistent with expectations from core accretion models that include internal feedback from the forming massive star.
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