On page 7 of NIST's views on SHA-3's security requirements and Evaluation of attacks, I see that, at least at this point, NIST planned on offering SHA-3 having eTCR security (defined on page 3):
eTCR: Find $M$ and then for a randomly chosen $r$, find $M’$ and $r’$ s.t. $H_r(M) = H_{r’}(M’), (r,M) ≠ (r’,M’)$ where $H_r$ is the randomized hash.
However, I never saw any subsequent references to the eTCR property for the SHA-3 candidates.
Does SHA-3 have an eTCR mode?