I think that, on the whole, it wouldn't be possible to stack multiple Fidelius Charms onto a single location (although it doesn't happen in canon so we don't know for sure). Firstly, that idea doesn't seem to be compatible with what the books tell us happens to Fidelius Charms once they are broken. And, secondly, the Charm is so complicated that I'm not sure it would be possible.
The mechanics of broken Fidelius Charms are important here. It seems that a Fidelius Charm ceases to exist when the people which it's protecting die.
He could see it; the Fidelius Charm must have died with James and Lily.
(Deathly Hallows, Chapter 17, Bathilda's Secret).
The Fidelius Charm continues to exist if the Secret Keeper dies - but everyone they've told also becomes a Secret Keeper.
Mr Weasley had explained that after the death of Dumbledore, their Secret Keeper, each of the people to whom Dumbledore had confided Grimmauld Place's location had become a Secret Keeper in turn.
"And as there are around twenty of us, that greatly dilutes the power of the Fidelius Charm. Twenty times as many opportunities for the Death Eaters to get the secret out of somebody. We can't expect it to hold much longer."
(Deathly Hallows, Chapter 6, The Ghoul in Pyjamas).
And, of course, the Fidelius Charm can partially break if the Secret Keeper reveals the secret to another person. This has to be done voluntarily, not under duress, and does not mean that that new person then becomes a Secret Keeper themselves (as per Pottermore).
Note that in the second and third instances the Fidelius Charm remains active and operational. It is just weakened by the secret being revealed to more and more people when obviously it is designed not to be revealed at all (or only to a small group of trusted people). Only once the people being protected die is the Fidelius Charm said to "die" itself. It could also be that Fidelius Charms elapse after a designated period but this is speculation and we don't know this.
All this means that, when someone who you wish didn't know your protected location finds out the secret, casting another Fidelius Charm is unlikely to keep them out. Why? Because the first Fidelius Charm is still operational. It has been weakened by the secret being shared but not terminated. Which means that the layering of Fidelius Charms is going to cause a lot of unknown and possibly chaotic side-effects.
Think about the practicalities involved. It's possible that the second Fidelius Charm would be rendered ineffective by the first, meaning that nothing would change and the person you wanted to keep out would still have access. It's possible that the confusion around the location would cause some kind of magical paradox, rendering the location visible at some times but not at others. It's even possible that the Charm may only show the location to people who know one secret but not the other - locking you out of your own house but granting access to the person you wanted to keep out! The consequences would be unforeseeable, which is hardly where you want to be with security. A far safer way forwards would be to evacuate and cast a fresh Fidelius Charm on a new location.
Anyway, multiple Fidelius Charms may not be possible.
Flitwick stresses the complexity of the magic involved when he describes the Charm.
"How does that work?" said Madame Rosmerta, breathless with interest. Professor Flitwick cleared his throat.
"An immensely complex spell," he said squeakily, involving the magical concealment of a secret inside a single, living soul."
(Prisoner of Azkaban, Chapter 10, The Marauder's Map).
Since casting one Fidelius Charm is an "immensely complex" feat you can imagine how complicated it might be to cast multiple Fidelius Charms on the same place. It may even be beyond the skills of someone of Dumbledore's calibre to pull off. As with other complex spells, like the Horcrux-creating spell, it seems that duplication multiplies complexity. This is tricky, tricky magic. Casting one Fidelius Charm would be beyond most. Casting multiple Charms on the same location may be impossible.