You could make many small vacuums in a honeycomb structure but at that point is just cheaper to use a lifting gas...

Honeycomb structures; may be dynamic and expanded as a sort of umbrella since pressure is lower higher up above the clouds. I guess a nifty construction with tiny small mirrors can direct lots of solar energy and work as sails, controlled by smart bending compliant mechanisms. Also - regarding flying objects, I've always wondered if a rotating disc, ie frisbee falls slower to thee ground because of atmosphere interaction, or if it's still falls slower in a vacuum with other forces at work. Well, still rails and boats are good stuff. I really like that honeycomb for an -n dimensional space construction idea.

Instead of additional mass, you could add additional energy.

For example, a small maglev running around the inside of the vacuum sphere would steady outward pressure on that part of the sphere. Add more trains at different angles to even out the forces.

As a bonus, this kind of "active structure" can dynamically vary its structural strength as atmospheric pressure changes with altitude or weather.

See Orbital Rings for more info.