"Head amp" is a term for a high gain device that will supplement a phono stage to provide enough gain for a low output moving coil. Sdcampbell has been around this hobby long enough, like me, to still know the term. You don't see references in the marketing materials to "head amp" much anymore.
Many companies today offer offer units that have more than 60db gain in the phono only. For example: Aesthetix, BAT, Herron, Lamm, Manley, Pass Labs, Tom Evans, and others offer units that have more than 60db gain in the phono only.
Also, consider the total gain of both the phono stage and the line stage when determining how much gain you have available.