Any way to wangle a look at Blenheim Palace off season?

The notoriously challenging nature of scheduling your holiday in the U.S., puts me in the U.K Mid-Late November. The first time I was in England was 1999 and I *desperately* wanted to see Blenheim Palace but it was closed then, as it will be now. Who knows how, if, or when I will ever be able to return to see it. It's a major trip from California, and I am motivated to find some way to see this beautiful place and the grounds. I do not want to invade the privacy of the owners, but I thought surely there could be privately booked events that I might contrive to gain admission to....? If nothing else, are the grounds open in some fashion? Would appreciate the advice of a well informed local... or a contact at a local business who could advise me, if it's impractical to post in the open on this site. (or even a creatively disguised temporary email address)