We propose the Posse¹ framework for optimizing incremental view maintenance at data warehouses. To this end, we show how for a particular method of consistent probing it is possible to have the power of SQL view queries with multiset semantics, and at the same time have available a spectrum of concurrency from none at all as in previously proposed solutions to the maximum concurrency obtained by issuing all probes in parallel. We then show how optimization of the probing process can be used to select various degrees of concurrency for the desired tradeoffs of concurrency against processing cost and message size.