The attack you describe---Joux's multicollisions, as far as I can tell---applies to Merkle-Damgard functions. SipHash is a spongy, wide-pipe, design where that

The attack you describe---Joux's multicollisions, as far as I can tell---applies to Merkle-Damgard functions. SipHash is a spongy, wide-pipe, design where that sort of thing doesn't work. The generic bound is (k!)^(1/k) ⋅ 2^(n(k-1)/k)) work to find a k-collision, or approximately k ⋅ 2^n for large k.