In ‘The Name of The Doctor’ Clara and the Doctor discover the future TARDIS. It is so big that Clara at first mistakes it for a monument. The Doctor realises the truth, that his ships dimension dams have broken causing a size leak.
The fact that there is a dimension dam suggests that the interior dimension of the TARDIS is naturally inclined to manifest in our dimension. It is the job of the dimension dam to hold it back.
We’ve always known that the TARDIS could change it exterior but what is the relation between its outside and its interior? The exterior is commonly referred to as an outer plasmic shell and its shape crafted by the chameleon circuit.
It isn’t clear whether the plasmic shell can be altered (maybe on a molecular level) or whether it swaps one shell for another from its interior (as suggested in the short story ‘The Little Things’).
When we see the TARDIS transform in ‘Attack Of The Cybermen’ the familiar police box fades away to reveal a new dresser shell, accompanied by a sound not unlike that of materialisation which would support the latter theory.
The fact that the exterior can grow suggests some exchange is taking place, as more mass it added to the plasmic shell. Since it remains in proportion there must be some adjustment made to it as this process continues.
What isn’t clear is if the interior is being converted into the exterior, in which case it would be half the size of the total interior when the dam in place. It is possible that once it achieves a balance the interior dimension stops spilling out. It is also possible that there is something else being converted (maybe the power within the TARDIS) that would allow the exterior and the interior to be exactly the same size.
So we know that a TARDIS can change its size. The Doctor’s own TARDIS was reduced to the only a few inches in ‘Planet of the Giants’, he shrinks the Meddling Monk’s TARDIS in ‘The Meddling Monk’, the Master has created a mobile giant stone robot with his TARDIS and Iris Wildthyme’s TARDIS took the form of London double decker bus.
Just how small or big could a TARDIS get? Presumably the smaller the TARDIS gets the greater the strain on the dimension dam, with the reverse being true as the TARDIS increases in size (which could be a way to save energy).
In theory the only limit is just how big the interior is. We know that it does have a finite space within itself, as over the years various parts of been ejected. It is also reasonable to suppose that there is only so big that it needs to be. It is, after all, primarily used to travel.
It is entirely possible that the interior is not static. If its exterior dimensions can be changed there is no reason why it couldn’t do the same for its interior. Since that space has to come from somewhere a TARDIS might take it from empty space (which is why we occasionally see the TARDIS hovering amongst the stars rather than travelling through the time vortex) and could have hastened universal entropy.
The TARDIS has shown an ability to reconfigure its interior layout and have some inclination of its own future, having multiple console rooms, including ones that the Doctor hasn’t used yet. It is possible that it anticipates its occupants needs before they do, reducing or increasing its interior space to accommodate this.
So the answer is that the interior is as big as it needs to be. Only someone who spends a long time in the TARDIS, for example the Doctor, would ever notice that it alters at all. Most would stay within specific areas, never venturing further to find its limits.
Conceivably, while the TARDIS is primarily designed to blend in and thus would prefer a small size, it could be much bigger. A TARDIS could be a building, a structure several miles high, a vast land mass or even a planet. Even if it blends in by changing its form people will notice.
Increasing a TARDIS’ exterior to such a size does put a new spin on the Doctor’s materialising around a real police box, replacing it. If a Time Lord wanted to isolate a building from the exterior or hide a planet from an invasion he could simply have his TARDIS appear around it, assuming its form.
Increasing the size of a TARDIS could also be used to terrify the locals or cause great damage. Certainly one can imagine this tactic being used during the Time War. There would be little defence to one or more mile high TARDIS’ suddenly materialising on a planet and smashing through buildings.
The fact that the Doctor recognises what has happened to his own TARDIS indicates that he has some knowledge of this type of thing and that it is connected to failing systems. This could be from early versions of the TARDIS or what happens to old models. It is also possible he saw the same thing happen to other TARDIS during the Time War.
An increase in size could be the first warning sign that PCs get that their own TARDIS is sick or dying. It could only a few inches at first, before growing bigger over time at a much faster rate.
They could also encounter the destruction caused by a giant TARDIS, whether as a malicious act or the death throe of a time machine. Whatever the reason the consequences would have a huge impact on the surrounding area.
If PCs realise the potential of changing the size of the exterior they may be tempted to use it as a way to solve a problem. They could ram alien spaceships or grow to shield a city. Such tactics are best reserved for drastic, one-off measures.
In a game where this is used too frequently you may wish to introduce some drawbacks. For example it could be that the exteriors invulnerability is linked to its size. The bigger it gets the more likely it is to be damaged.
You could have the dimension dam damaged, either locking it at its current size or preventing it from being shrunk. Reducing the interior dimension so that it is smaller than its exterior would also prevent the PCs from increasing the size of its exterior for fear of crushing themselves.