Classical protocols for reliable broadcast and consensus provide security guarantees as long as the number of corrupted parties f is bounded by a single given threshold t. If f>t, these protocols are completely deemed insecure. We consider the relaxed notion of \emph{multi-threshold} reliable broadcast and consensus where validity, consistency and termination are guaranteed as long as f≤tv, f≤tc and f≤tt respectively. For consensus, we consider both variants of (1−ϵ)-consensus and \emph{almost-surely terminating} consensus, where termination is guaranteed with probability (1−ϵ) and 1, respectively. We give a very complete characterization for these primitives in the asynchronous setting and with no signatures: -Multi-threshold reliable broadcast is possible if and only if maxtc,tv+2tt<n . -Multi-threshold almost-surely consensus is possible if maxtc,tv+2tt<n, 2tv+tt<n and tt<n/3. Assuming a global coin, it is possible if and only if maxtc,tv+2tt<n and 2tv+tt<n. -Multi-threshold (1−ϵ)-consensus is possible if and only if maxtc,tv+2tt<n and 2tv+tt<n.