Take a page from String Theory
There are many flavours of String Theory. My favorite is called type IIB, for two reasons: it reminds me of a very lovely robot and it has a very creative quantum description of black holes.
In general relativity, a black hole is a body so dense that it has an event horizon: a region around it with an escape velocity greater than that of light. That necessitates a singularity at the center and creates more troubles for physics than it solves. You read enough about this, and you get ideas about wormholes, time travel and information paradoxes.
In IIB, a black hole is more properly described as a fuzzball. The whole of the black hole is its surface (the event horizon). There is no inside. From PBS Spacetime (one of my favorite shows) (also the emphasis below is mine):
As a fuzzball is forming, all of the matter - now dissolved into stringy mess, is pushed up to the surface and the interior grid of spacetime is deleted from the universe.
Funny thing: the reason why the fuzzball has, externally, all the same properties as your regular black hole is that it behaves kinda like an interiorless katamari: everything that touches it becomes part of it, including light. Unlike a katamari, though, it won't break if you hit it with any force at all.
IIB also stipulates that the universe has 10 dimensions (or branes), with four being time and space, and the other six being really compacted. These dimensions can be distorted just like the strings in them, which is what allows for the fuzzball to be a region of space with no inside.
Just the same, it is very theoretically possible to poke a hole into a fuzzball and then refill the space inside it. And the space inside can then become arbitrarily large, not being bound by the outside in any manner. You can also loop the branes inside. You can have a separate, possibly infinite universe in there if you mess around enough.
Now, regardless of what is inside, the outside will only ever notice the mass of the fuzzball itself (without the contents of the branes you put in)! Just the same, those inside will not notice anything from the universe outside. The only interaction between the inside and outside is through the aperture through which you inserted the branes. Close the gap, and you have two parallel universes.
The only thing you need now to avoid killing everyone in a very messy manner is to put some surface over the fuzzball so that people don't touch it, because remember: you touch it, you become part of it FOREVER. No, really: every string that makes the particles in your body gets disassembled and is absorbed by the more complex strings forming the fuzzball. There is no going back.
So in order to make Newt's suitcase, for example:
- Make a microscopic black hole. For comparison, a coin-sized one might be as massive as the Earth. We are really talking microscopic here so it weights no more than a suitcase.
- Contain it somehow (static, maybe? Black holes can have electric charge). Make the container look like a suitcase.
- Poke a hole on the fuzzball. This is the magic part of this, as even string theory offers little help here (even though it kinda implies it is possible).
- Insert some branes (i.e.: spacetime and other dimensions) into the hole.
- Stretch the aperture of the fuzzball to fit the open suitcase, and stretch the inside as well.
- If you want the inside to have comfortable gravity, you can either make it spin (makes keeping the opening relatively static complex), or have a planet inside the fuzzball and build the "interior" of the suitcase on top of it.