I'm afraid the current REST api doesn't have anything to describe the CV, you can't use the regular endpoint to discover which parameters are required.
BUT! This is OneStream, there is always a hack. You can use the other GetAdoDataSet* calls to query the OneStream database to retrieve any information you need. CubeViews are in the CubeViewItem application table, where the field XmlData contains the entire CV description. You can retrieve that via REST, parse it to figure out the parameters, and then react.
From a performance perspective, the best way to do this would probably be to set up a Dashboard DataSet that uses SQL Parameterized Queries, then call it through GetAdoDataSetForMethodCommand. If that is too much bother (i.e. if this stuff is not called several times a day), you can just use GetAdoDataSetForSqlCommand or GetAdoDataSetForAdapter (calling a SQL adapter) instead, executing raw unoptimized SQL.
