Inspired by some fan art, I was considering how possible it is to create a TARDIS using Harry Potter magic. Time travel seems to be nearly impossible, (Time-Turners are extremely limited in use, and only seem to let you go backward), but just about everything else seems doable.
Step 1: Find a blue police box.
Step 2: Use the charm to make it bigger on the inside (just like the wizards' car trunks or tents).
Step 3: Enchant it to fly (like the Weasley's car).
Step 4: Put a protective enchantment on it like the one on Hogwarts that makes muggles ignore or overlook it (analogous to the chameleon circuit's properties in the Whoniverse)
But in order to get the disappearing/reappearing effect the Tardis has, Step 5 would be to turn it into a portkey every time you want to teleport somewhere (there are the legal issues with authorizing said portkey with the ministry, but I'm ignoring that issue). All the portkeys we see in the books are small objects that can be held onto while they teleport, is it possible to turn a large object like a phonebox into a portkey and teleport inside it?