Is it possible to move into another dimension?

Only if you have the right moving company.

Consider a piece of paper on the desk. It has four dimensions but is said to be two dimensional. The same with us, we already exist in all dimensions. There are eight known ways of measuring things that we use already:

Length, width, height, weight, temperature, velocity, time and heat.

We are on the threshold of understanding the relationship between them and how the law of conservation relates to all.

Our reality like the piece of paper exists in a larger reality. It is already existing in all the dimensions of that reality, but we can not relate to how the total is seen. That reality would be one where all universes exist at the same time. Just as a stack of papers can be seen in our reality.

So maybe what you are asking is if you can move to another reality!

First it is not a given other realities exist. They might be a function of time, meaning we co-exist with ourselves in the same universe. If they do exist then travel would only be possible if we learn a mechanism that allows travel.

It is impossible to say what will be possible in the future, but for now the answer is NO!