It is indeed possible if your definition of a multi-input XOR is: result is high if exactly one of the inputs is high. For 3 inputs, in boolean algebra, given inputs a, b, and c, and output y (& = AND, ^ = XOR, | = OR):

y = ((a ^ b) ^ c) ^ (a & b & c)

This can be expanded to support four inputs:

y = (((a ^ b) ^ c) ^ d) ^ (a & b & c & d) ^ ((a & b & c) | (b & c & d) | (a & c & d) | (a & b & d))

and so on. It's provable by running it through a truth table.

A 3 input XOR as a circuit:
View attachment 91416

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