Is there such a thing as a variable density beamsplitter?

Yes. A variable density beamsplitter has linearly varying reflection and transmission percentages across its length. Actually any neutral density filter with a metallic coating (typically inconel) can be used as a beamsplitter. Catalog values state optical densities at a 0° (or normal) angle of incidence, which can be quickly converted to transmission values (see Frequently Asked Questions on filters). The coating is designed to transmit a specific amount of energy, but as a result of the metallic coating a certain amount will be reflected. When using a filter of this nature as a beamsplitter, please note that absorption characteristics and changes of angle (0° to 45°) will dramatically affect the actual reflection/transmission energy split. Edmund Optics offers a linear Variable Density Beamsplitter that is primarily used as a variable neutral density filter.