Understanding merging

I work with a very senior colleague who has never always resisted
version control and would much rather do without it, but he is forced to
go along and I am the whipping boy whenever something goes wrong.

He poses a general but simple question that I find myself unable to give
a simple answer to. I am rephrasing it slightly but it bothers me that
I don't know the simple answer. If I found myself in this situation I
would tweak until it was as desired, but my persnickety colleague is not
satisfied with such answers and for once, I don't blame him.

Given two branches off a trunk that were taken at different times, if
the first is merged back to the trunk and then the second, how may the
second be merged back into the trunk so as not to override changes from
the first merge, assuming that both change sets are desired to be in the
trunk at the end?