  We show that the previously obtained subtracted geometry of four-dimensional
asymptotically flat multi-charged rotating black holes, whose massless wave
equation exhibit $SL(2,\R) \times SL(2,\R) \times SO(3)$ symmetry may be
obtained by a suitable scaling limit of certain asymptotically flat
multi-charged rotating black holes, which is reminiscent of near-extreme black
holes in the dilute gas approximation. The co-homogeneity-two geometry is
supported by a dilation field and two (electric) gauge-field strengths. We also
point out that these subtracted geometries can be obtained as a particular
Harrison transformation of the original black holes. Furthermore the subtracted
metrics are asymptotically conical (AC), like global monopoles, thus describing
"a black hole in an AC box". Finally we account for the the emergence of the
$SL(2,\R) \times SL(2,\R) \times SO(3)$ symmetry as a consequence of the
subtracted metrics being Kaluza-Klein type quotients of $ AdS_3\times 4 S^3$.
We demonstrate that similar properties hold for five-dimensional black holes.
