You also can't supply custom queries via custom visuals - it's the combination of data roles, data view mapping (from capabilities) and any filters that you apply in the visual that get passed to Power BI for delegation. Power BI will determine what DAX to run.
The filtering APIs have the same functionality as the filter pane in the UI, so if you can generate the desired result in a visual manually using an advanced filter then you can use the Advanced Filtering API to generate an IAdvancedFilterCondition for each column and specify whether they should be an AND or an OR operation in the AdvancedFilterLogicalOperators property. This behaviour could then be wired up in a custom visual based on selections of displayed data values, to form a slicer, if you want this on the canvas rather then using the filter pane.
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Don't have an answer but I am curious to learn about the use case. To me this feels like a solution in search of a problem, and something that can potentially confuse the report users (as they may have different expectations).