Looks like a spot for a serious collection. You could take some of the shelves out. Display some framed photos or art along with a few chosen objects. Some attractive boxes or baskets on the bottom.

"It would be nice to have something enclosed " Are you needing a hall closet? Taking all the shelves out, putting solid doors on would give you what you want w/o ripping into the walls. The tiered top is odd and that would remain. or you have it removed and a taller box/closet built but a corner closet would be odd.

Wow someone must have really loved their treasures to create this beautiful big cabinet for them.

How close it is to the entrance? How big is your entrance? What is the rest of the decor in your space? Can you use it? Would it hinder your entry way and the way you decorate? Is this in an odd corner to begin with? Is it smaller than it looks? It appears to be brought forward and maybe that extra space behind is something you would rather see than covered by this large cabinet.

Do you like it? Are there three types of wood in the space? I see the ceiling looks slightly different than the wood trim and wood floors. By the way love the wood floors.

A few photos further back might help others to see what you see and how it will hurt or help you space? Maybe painted all the same color might make it more appealing but again this depends on your style. Maybe a drawing of size in relation to the size of your entrance.

Some wizard on Houzz will come up with a great idea of how to design remove or work with it.

I would love to have that in an entry way. I would put some type of collection into it, if it were mine. Its really very pretty.

I would need context and info from you to advise. For me a rip out but maybe a use for it somewhere else like a walk in closet for purses and accessories for instance .It seems an odd spot for diplay but the previous owners maybe had something important to them

I would def want to remove it but first I would want to make sure the flooring continues beneath it -

If you plan on removing, have you checked if the flooring continues under the cabinet? Or if you keep, do you have a collection of something you'd like to display?

What about removing the upper soffits entirely and just adding some wider Colonial crown molding to the top? Then I'd paint the whole thing to match the wall color. I'd go with a brighter white.

Something like the ceiling crown molding, here:

Horse Country Home · More Info

Those soffit thingies are just bulky and odd-looking.

I would demolish the top section down to the wood crown moulding. Then find interesting items to place in the cabinet (items you like, already own such as travel souvenirs, art or photos in frames, etc.)

This is a great place to put a collection that makes you smile when you walk in the door. It is not the place to park boring things that you feel obliged to keep or have bought at Home Goods simply to fill up space. Travel souvenirs, pretty rocks and fossils, Star Wars figures, wabi-sabi pottery, handmade quilts- whatever takes your fancy.

Is it possible that there is some sort of ductwork running in the diagonal wall at the back? This seems really odd to me. And why the stepped portion above? I would strip it out completely.

I would remove it. Odd looking for a house. Looks like a museum case. Or a store display case.