High-temperature chlorination of conventional IPR C60 can produce chloro derivatives of non-IPR C60 by skeletal transformations via Stone-Wales rearrangements (SWRs) of the carbon cage. We report the synthesis and structure elucidation of non-IPR 1809C60Cl8 and nonclassical C60(NC)Cl14. The present isolation of 1809C60Cl8 hints at the possibility that the same product in the previously reported chlorine-doped arc-discharge synthesis could have, likewise, resulted from the initially formed IPR C60. C60(NC)Cl14 is the first chloride containing a nonclassical carbon cage with one heptagon and 13 pentagons known previously only in a CF3 derivative. Additionally, trifluoromethylation of non-IPR chlorides revealed the formation of 1806C60(CF3)14 with a new non-IPR carbon cage and unusual trifluoromethylation pattern. Thereby, the number of different, structurally confirmed non-IPR carbon cages of C60 now reaches eight.