[Vocabulary] What does 'Beyond' mean in this sentence

[gaolei]

The great advantage of taking medicine is that it makes no demands on the taker beyondthat of putting up for a moment witha disgusting taste.
What’s meaning of ‘beyond’ here?

I found a relevant explanation in dictionary:
You use beyond to introduce an exception to what you aresaying
For example: He appears to have almost no personal staff,beyond a secretary who can't make coffee

What I understand about meaning of ‘beyond’ is right?

Then, what does ‘that’ in the phase ‘beyond that of ‘stand for?
Does ‘that’ stand for ‘demand’?
Can I say like this?
The great advantage of taking medicine is that it makes no demandson the taker beyond a demand of putting up for amoment with a disgusting taste.
He appears to have almost no personal staff beyond a person of a secretary who can't make coffee.

Last, what does 'putting up' mean? Does it mean suffering?

 

[jutfrank]

beyond that of means 'except for the demand of'.

beyond a secretary means 'except for a secretary'.

putting up with means 'bearing' or 'tolerating'.