  We study revenue maximization for agents with additive preferences, subject
to downward-closed constraints on the set of feasible allocations. In seminal
work, Alaei~\cite{alaei2014bayesian} introduced a powerful multi-to-single
agent reduction based on an ex-ante relaxation of the multi-agent problem. This
reduction employs a rounding procedure which is an online contention resolution
scheme (OCRS) in disguise, a now widely-used method for rounding fractional
solutions in online Bayesian and stochastic optimization problems. In this
paper, we leverage our vantage point, 10 years after the work of Alaei, with a
rich OCRS toolkit and modern approaches to analyzing multi-agent mechanisms; we
introduce a general framework for designing non-sequential and sequential
multi-agent, revenue-maximizing mechanisms, capturing a wide variety of
problems Alaei's framework could not address. Our framework uses an
\emph{interim} relaxation, that is rounded to a feasible mechanism using what
we call a two-level OCRS, which allows for some structured dependence between
the activation of its input elements. For a wide family of constraints, we can
construct such schemes using existing OCRSs as a black box; for other
constraints, such as knapsack, we construct such schemes from scratch. We
demonstrate numerous applications of our framework, including a sequential
mechanism that guarantees a $\frac{2e}{e-1} \approx 3.16$ approximation to the
optimal revenue for the case of additive agents subject to matroid feasibility
constraints. We also show how our framework can be easily extended to
multi-parameter procurement auctions, where we provide an OCRS for Stochastic
Knapsack that might be of independent interest.
