For intricate or elaborate:
* Intricate
* Elaborate
* Complicated
* Sophisticated
* Involved
* Multifaceted
* Multilayered
* Detailed
* Nuance
For difficult to understand:
* Confusing
* Arcane
* Obscure
* Cryptic
* Abstruse
* Knotty
* Tangled
For having multiple parts or components:
* Compound
* Composite
* Multipartite
* Composite
* Structured
For psychological or emotional:
* Complicated
* Twisted
* Troubled
* Multifaceted
* Conflicted
For a building or structure:
* Elaborate
* Ornate
* Grand
* Majestic
It's important to choose the synonym that best fits the specific meaning you want to convey.