A word/phrase for something massively complex

Solution 1:

Convoluted? (especially of an argument, story, or sentence) extremely complex and difficult to follow.

It covers the 'massively complex' meaning and also covers the 'poorly organized' meaning too (difficult to follow).

Solution 2:

It's highly informal, but byzantine is a near-fit for what you're looking for.

Byz·an·tine

ˈbizənˌtēn,ˈbizənˌtīn/

adjective

adjective: Byzantine

1.of or relating to Byzantium, the Byzantine Empire, or the Eastern Orthodox Church.

2.(of a system or situation) excessively complicated, typically involving a great deal of administrative detail.

Solution 3:

If you're familiar with some of the classic Western legends and myths, then maybe "Gordian" or "Gordian Knot" might ring some bells. Of course, that story also provides a potential solution -- incisive (hehe) force. Of course, your audience may not be familiar with the story... https://en.wikipedia.org/wiki/Gordian_Knot

"Labyrinthine" could also work, especially if you are referring to a complex space.

"Chaotic" could work, but it's also rather common and abused.

Or perhaps something like "slapdash monstrosity" might tickle your fancy.

Solution 4:

Rat's nest might be a more informal description, and of a lighter degree.

Implies that something has been constructed in a way that is a complete mess, with all kinds of different bits and pieces cobbled together, just like a rat's nest.

I work in web development, and we use this term to describe some of the projects we step in to work on.