Force user context of a process which is not yet launched

Force user context of a process which is not yet launched

I don't think that there might be a solution for what I want to do but you
never know :) I have an InstallShield Setup which is being launched from a
service running in system context. The setup launches an exe file through
an InstallScript function (cannot change that unfortunately) with a bunch
of parameters but this does also happen in system context. My question is,
is there some way to detect if the process launches and force it to run as
the currently logged on user? I've got some basic C# knowledge so if there
is maybe a way to do this programatically I'd also be happy for
suggestions going this way.
Thanks so long!