As of my latest read, there are two types of non-BCTs brigade level units in the US Army: Modular Multi-function Support Brigades and Functional Brigades.

There are 100 Modular Brigades across the three components Active, National Guard and Army Reserve. The types are: Fires, Combat Aviation (with four sub-types), Maneuver Enhancement (MPs, ENG, NBC), Sustainment (CSS minus Medical), and Battlefield Survelliance (MI with a sprinkling of Cavalry).

There 127 Functional Briages of 11 types: EOD, MP, CID, ADA, NBC, ENG, MI, POL, SIG, MED, and Theater Aviation.

Seems that as a general rule of thumb, modular divisions are built using BCTs and modular briagdes and Corps/theater troops are from the functional briagde pool. Not to say you will not see a functional brigade assigned to a division. But only very seldom will a modular brigade be under Corps control.

Lots of powering down to enable divisions to fight the fight. Corps seem to be the focus of Joint and Combined operations vice conducting their own operations.

Pretty much gone are the Corps Deep Attacks with helos and MLRS. Now, Corps gives the mission/task to the appropriate division to plan and execute.

What went out with transformation/modualization was:

The Division "Base" (MI Bn, Engineer Bn, Signal Bn, ADA Bn, Cav Sqdrn, Band, MP Co), DISCOMs and COSCOMs, DIVARTYs and Corps Artillery, Division Cavalry and ACRs,

At the action/execute level, these have been replaced by Sustainment Brigades, Fires Brigades and to a much lesser extent Battlefield Survelliance Brigades. Planning responsibilities are bit murkier.