The most common and most likely answer to this crossword clue is the 10 letter word SPACE-TIME
I've seen this crossword clue in The Guardian
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More clues leading to the result SPACE-TIME
Buddy explains!

The straight part
We know that "multidimensional" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case multidimensional = space-time.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SPACE-TIME mean?
SPACE-TIME noun- The four-dimensional continuum of the three spatial dimensions plus time.
- An n-dimensional continuum consisting of dimensions of both space and time. Normally spacetime is considered as having 4 dimensions (x, y, z, t), but higher-dimensional spacetimes are often encountered in theoretical physics, e.g. the 5-dimensional spacetime of Kaluza-Klein theory or the 11 dimensions of spacetime in M-theory.
- A specific region of the universe with mathematically different properties than the surrounding spacetime. Synonymous with "metric" within the context of general relativity.