Do you know if the Sienna is in the seven- or eight-passenger configuration? If the latter, which has a second row bench seat instead of two captain's chairs, you could cram three people into the second row and fold down the entire third row. This should give you plenty of luggage capacity.
If it's the seven-passenger configuration (which I believe is more likely), then you will need to use at least part of the third row for seating. It does fold down in two sections, however, so if someone can squeeze into the small part you would have about 60% of the full width in the cargo area and a smaller section behind the one seat. That should hold a lot of luggage too.
If you have to have the entire third row up or even the larger part up, things might be a little tight. You can put a fair amount of luggage in the bottom of the rear area, but you can't stack too much too high because of the slant of the rear door. Depending on the size of the suitcases and how creative you are, you might be able to get four larger suitcases and a few smaller pieces in the rear area with the entire third row in seating position. There probably would be room in the rest of the cabin for a few more bags.