The many-to-one mapping cited in support only holds for finite, co-equinumerous concepts, but Hume's Principle is unrestricted and applies to all concepts, including those individuating each distinct cardinal, forcing a domain at least as large as the full concept domain.

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Co-equinumerous(as used in mathematics and philosophy): Having the same number of members or elements; two groups are co-equinumerous if you can pair up each item in one group with exactly one item in the other.
Hume's Principle(Philosophy of mathematics, neo-logicism): A principle codifying the condition under which two concepts are equinumerous, namely when the number of objects falling under each concept is identical
Many-to-one mapping(as used in logic and mathematics): A situation where multiple different things (inputs) all correspond to or point to the same single thing (output)—like how many different ways to describe a color might all refer to the same color itself.
Unrestricted(logic/philosophy): Without limits or exceptions; applying everywhere and in all cases rather than just in special situations.

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