Small vias, fancy stencils and via patterns, special paste compositions, peelable masks ... with a combination of these and an additional investment in assembly NRE for each different product you can come up with a workable solution. What remains is that you are in effect specifying a known failure mode by design and leaving it up to your manufacturer to resolve. I will concede that if your product is targeted for a single manufacturer and is very high volume perhaps there is payback after all costs are considered. 

Or you can just specify filled and plated vias at fabrication and know you will have 100% repeatable results and a product that can be transitioned between manufacturers without issue. And usually more cost effectively.
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