  Recently, Thomas Hofweber (2005, 2016) has claimed to have found the required pair of readings.  A quantifier, he claims, may have either a domain-conditions or inferential role reading. The domain-conditions reading is just the familiar reading we know from first order semantics: ‘there are Fs’ is true iff there exists an entity in the relevant real domain which satisfies ‘F’.  This reading is therefore ontologically committing and so deep (and thus external).  The inferential reading, by contrast, brings with it no ontological commitment, and so is shallow (and thus internal).