We present the notion of multilevel slashing, where proof-of-stake blockchain validators can obtain gradual levels of assurance that a certain block is bound to be finalized in a global consensus procedure, unless an increasing and optimally large number of Byzantine processes have their staked assets slashed -- that is, deducted -- due to provably incorrect behavior. Our construction is a highly parameterized generalization of combinatorial intersection systems based on finite projective spaces, with asymptotic high availability and optimal slashing properties. Even under weak conditions, we show that our construction has asymptotically optimal slashing properties with respect to message complexity and validator load; this result also illustrates a fundamental trade off between message complexity, load, and slashing. In addition, we show that any intersection system whose ground elements are disjoint subsets of nodes (e.g. "committees" in committee-based consensus protocols) has asymptotic high availability under similarly weak conditions. Finally, our multilevel construction gives the flexibility to blockchain validators to decide how many "levels" of finalization assurance they wish to obtain. This functionality can be seen either as (i) a form of an early, slashing-based block finalization; or (ii) a service to support reorg tolerance.