India
Additional Superintendent of Police or Additional Deputy Commissioner of Police (Addl. S.P. or Addl.D.C.P.) is still in use in India where the officer holding this rank can be from Indian Police Service or from Indian States Police Services like West Bengal police Service(W.B.P.S.), Odisha Police Service(O.P.S.), Maharashtra Police Service(M.P.S.) etc.
The rank above it is Superintendent of police (S.P.) or Deputy commissioner of police (D.C.P.), and the rank below it is Deputy superintendent of Police (Dy.S.P. / D.S.P. ) or A.C.P.(Assistant Commissioner of Police)
References
Additional superintendent of police Wikipedia(Text) CC BY-SA