Would you deem the construct with ausmachen semantically and grammatically correct:
Könnten Sie darauf achten, dass ihm keiner etwas ausmacht?
Maybe we can say
Könnten Sie darauf achten, dass ihm niemand etwas ausmacht?
or
Könnten Sie darauf achten, dass er nichts ausgemacht wird?
What will be competing expressions?
The first two sentences are syntactically correct, but semantically wrong because ausmachen is not used in this way.
Ausmachen can have the meaning of "to bother" but it is generally used with actions and things, not with persons. It does not express the objective action of bothering someone but rather causing the subjective feeling of being bothered. An example for correct usage would be:
Macht es Ihnen etwas aus, wenn ich das Fenster schließe?
When it's about persons, stören should be used instead. Stören also has the benefit of being easier to use, taking only one object instead of two.
The third sentence is syntactically wrong because er is incorrect here. See the question Can you say “Ich wurde (etwas) gegeben”?
Your question lacks context, one can only guess what you want to express. As RHa explained, only the first two sentences are syntactically correct. You could understand them as Bodo and user unknown have suggested in their comments, in the sense that "etwas ausmacht" means "etwas abschaltet" (switch off something which is important for the person).
Most likely you want to say
Could you take care that nobody disturbs him.
This would be
Könnten Sie darauf achten, dass ihn keiner stört.
I guess you used the verb "ausmachen" because one correctly says
Es macht ihm nicht aus / Es macht ihm etwas aus
which comes very close to
Es stört ihn nicht / Es stört ihn
