See also: "Shared Source"
Might get away with it but maybe need alternatives. If not "open source" or "shared source," what's a generic phrase for software that includes the source but not necessarily OSS principles.
A free software (often copyleft) core with addons, which usually means that contributions to the core are riddled with CLAs or other hurdles, if possible at all.
See mysql, openoffice (pre-Apache), ...
"Published source"?