I doubt this list is original, but I haven't seen it before...
Most wickets+catches in a Test series:
51: Sydney Barnes, E v SA (1913-14): 49+2
50: Terry Alderman, A v E (1981): 42+8
48: Bert Vogler, SA v E (1909-10): 36+12
47: Clarrie Grimmett, A v SA (1935-36): 44+3
46: Ian Botham, E v A (1981): 34+12
46: Jim Laker, E v A (1956): 46+0
45: Shane Warne, A v E (2005): 40+5
44: Imran Khan, P v I (1982-83): 40+4
43: Terry Alderman, A v E (1989): 41+2
42: Hugh Tayfield, SA v E (1956-57): 37+5
41: Rodney Hogg, A v E (1978-79): 41+0
41: Mitchell Johnson, A v E (2013-14): 37+4
41: George Lohmann, E v SA (1895-96): 35+6
41: Arthur Mailey, A v E (1920-21): 36+5
40: Alec Bedser, E v A (1953): 39+1
40: George Giffen, A v E (1894-95): 34+6
40: Dennis Lillee, A v E (1981): 39+1
40: Tony Lock, E v NZ (1958): 34+6
40: Vinoo Mankad, I v E (1951-52): 34+6
If you count the Triangular Tests in 1912 as a single series, Barnes gets in the list again with 39+4.