[pushkins]

Yes if you sistered for example 2x8's to the existing 2x6's and could get them to span to a wall below so the the 2x8's could rest on that wall then that would do the trick nicely.
In fact if you could get the 2x8" 's to sister and sit on a wall you could store a great deal more "stuff" up there safely.

You cannot tho just simply sister the 2x8 's to the existing 2x6's and expect to increase the load if both ends are unsupported.

My suggestion in this unsupported sistering was for your pull down ladder and I also suggest that the NEW 2x8" 's span as far as possible.