Egypt actually has two kinds of "sphinx". Both are representations of the Pharaoh − the head is always the head of this king.
(It would make sense to have a womans head when the pharaoh is a queen, but I am unaware of an archeological example. Hatshepsut has depictions of herself on sphinxes, but she presents herself as male, with the pharaonic beard in her iconography.)
The famous sphinx, such as the one in the Giza complex, is the "reclining" sphinx. This is the body of a lion, and is the Pharaoh as relaxed, empowered, and secure.
The other kind of Egyptian sphinx is standing on all fours, and with falcon wings. This kind of sphinx is the body of a leopard (or panther). Here the Pharaoh as a fierce and mobile warrior.
Wherever a sphinx is, the pharaoh is magically present, so there can be many.
Here is an example of the striding sphinx from Tutankhamun. The wings are folded and appear here decoratively. Elsewhere the wings spread. This one has black fur, other examples have spotted fur. Examples of the winged sphinx are as early as the Intermediate 2 Period.
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Here is a scarab where Pharaoh Thutmose 3 appears as a sphinx, with wings clearly extending. Note the slim body of the leopard.
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There are examples of Canaanite sphinxes, which appear to be the same thing as the Egyptian winged sphinx.
Definitely the D&D Sphinx should be Celestial.