I realise this might be a stretch - and I debated whether it should just be a comment, but I would run into the character limit, since reasoning might take a bit:
Technically Dumbledore was in possession of all three Hallows at the same time once, or at least almost, again depending on the definitions of ownership and possession.
In German legal speak there is the term of "mittelbarer Besitz", which - according to Wang, German Civil Code, London 1907 - translates to "indirect possession". Kind of like if you walk a dog, and it wears a collar, you indirectly possess the collar.
Thinking about this led me to the following conclusion:
When Dumbledore collected Harry from Privet Drive before Harry's 6th year (in HBP) and they side-alonged, Dumbledore was indirectly in possession of The Cloak, which Harry was carrying (i.e. owning and "directly possessing") while being carried/dragged-along by Dumbledore, who wore the recently retrieved Resurrection Stone to impress Slughorn and of course also still carried, therefore possessed (and owned) the Elder Wand.
"[...] However, I would like you to bring your Invisibility Cloak… just in case.”
Harry extracted his cloak from his trunk [...] stuffed it into an inside pocket of his jacket, Dumbiedore waved his wand [...] --HBP, Ch.3 - Will and Won't
At the very least, we can be reasonably certain that this was probably the closest together physically the three Hallows were since their creation: Harry extracts the cloak from his trunk while Dumbledore wears the Ring and wields the Wand. That is the only point in the story I can recall when all of them would be visible to an observer at the same time. Which they were never again afterwards (at least until someone finds the Stone in the Forest, steals the Wand from the Tomb (again) and steals the Cloak from whoever will then own it, of course).