Sure you can! This is typically called a 'Coffered Ceiling' - and even though these beams appear to be structural, most of the time they are just constructed out of trim material to give this appearance.

Before you get your trim guy to start nailing stuff to the ceiling, you should first think about how you want to lay out the pattern so that it is symmetrical and makes sense with other components in the room - like fireplaces or door openings. The depth of the beams can also vary, so if you don't have a high ceiling like the 10' ceiling in this picture, you might want to make the beams not so deep. So maybe 6" deep instead of 10" like these are. Do a search in Houzz for 'coffered ceilings' and you will see lots of different variations.

Lastly, you'll need to make sure you have something structural to fasten the beams to - like floor joists for the floor above, or ceiling joists if the room is the top level.

Let us know if you have any other questions!

Dale