Is it possible for 3-dimensional beings that exist within an n-dimensional universe (n>4) to build 4-dimensional...

You'd have to define what you mean by "3-dimensional beings."

Think of the problem in terms of 2D versus 3D. Imagine a 2D plane stretching through a 3D universe and that plane is full of "2D beings." What does that mean for those beings? If you take it to mean that they are confined to that 2D plane, then they obviously could never even be aware of that third dimension all around them. But if your definition allows them to somehow rotate their bodies on an axis (a 1D line within their 2D plane), then they could escape that plane and move around in the third dimension. They would never be able to directly perceive anything in three dimensions, though, because all their sensory organs are still 2D. So they'd see slices of the 3D universe and have to try to imagine what it all meant.

Is it theoretically possible for 3-d entities to combine 3-dimensional objects in such a way that would add an extra dimension to them?

Again, define "dimension" here.

As annoying it may be, if you want to have a discussion, you need to define what you think of as a dimension and an n-dimensional being. One definition I know involves vector spaces, I'm sure you've heard of it.

Only if you allow them to move one of those 3D objects along the fourth spacial axis.

here u go m8

3-d beings that have access to technology that can bend their space, only they wouldn't be able to perceive any of that, as their senses are also part of the process.

you are a brainlet

There cannot be an "n-1" dimensional being in an N dimensional space, because it automatically utilizes all of that Universe's dimensions - its information will always be defined as points situated within as many dimensions as the parent.

Even if something was infinitely flat in our Universe, it's still technically not exclusively 2D because it moves both in 3D and 4D (time), which is an indicator that its dimensions haven't been reduced other than it having slightly less depth than the rest.

An n-dimensional space is a space that requires n coordinates to define ever object in it

So that would be like the 2D beings in the 2D plane universe being able to bend that plane in the 3rd dimension. So you could imagine them constructing a 3D object by gradually moving a part of their universe up and down within our 3D universe.

Here's a big problem they're going to face, though... All their atoms are 2D. So every "slice" of the 3D object that they build is infinitely thin. They would need to find a way to push around 3D atoms from within their 2D plane.