  We extend the analysis of arXiv:0801.4457 [hep-th] to charged black hole
solutions of four-dimensional $U(1)^4$ gauged supergravity which carry three
charges. There are two decoupling near-horizon limits, one over the near-BPS
black hole solution and the other over the near-extremal, but non-BPS geometry.
Taking the limit over the eleven dimensional uplift of these black hole
solutions, for both of these cases we obtain a geometry which has a piece
(conformal) to rotating BTZ $\times S^2$. We study the 4d, $11d$ and $5d, 3d$
black hole properties. Moreover, we show that the BTZ$\times S^2$ geometry
obtained after the near-BPS (near-extremal) limit is also a solution to
five-dimensional $U(1)^3$ un-gauged (gauged) STU supergravity. Based on these
decoupling limits we argue that there should be sectors of 3d CFT resulting
from low energy limit of theory on $N$ M2-branes ($N\to \infty)$, which are
decoupled from the rest of the theory and are effectively described by a 2d
CFT. The central charge of the 2d CFT in both near-BPS and near-extremal case
scales as $N$. The engineering dimension of the operators in these decoupled
sectors scales as $N^{4/3}$ (for near-BPS case) while as $N^{3/2}$ (for the
near-extremal case). Moreover, we discuss the description of the decoupled
sectors as certain deformations of $6d$ CFT residing on the intersecting
M5-brane giants.
