Actually, re-reading the post I think that by ‘parts’ you didn’t necessarily mean ‘temporal parts’. In particular, your example of Alice suggests that in that case, the ‘parts’ in question are ‘people’. Broome has a parallel view to ‘separability of times’, called ‘separability of lives’ and discussed in ch. 8 of Weighing Lives, which corresponds to this use of ‘parts’.
Actually, re-reading the post I think that by ‘parts’ you didn’t necessarily mean ‘temporal parts’. In particular, your example of Alice suggests that in that case, the ‘parts’ in question are ‘people’. Broome has a parallel view to ‘separability of times’, called ‘separability of lives’ and discussed in ch. 8 of Weighing Lives, which corresponds to this use of ‘parts’.