Can I use two different possessive nouns that are taking about the same possession?

This turns on the way the reactions are, in fact, individual. Your friend John and brother Jack have different reactions, though they may be the same. Therefore you can use two possessive nouns. If they did, in fact, own the same thing, only the last one would get the possessive

Like this:

A less-often faced decision involves the use of apostrophes where multiple owners are named. Where two or more people own one item together, place an apostrophe before an "s" only after the second-named person. For example:

Incorrect: Bill's and Mary's car was a lemon, leading them to seek rescission of their contract under the state's lemon law.

Correct: Bill and Mary's car was a lemon, leading them to seek rescission of their contract under the state's lemon law.

However, when two or more people own two or more items separately, each individual's name should take the possessive form. For example:

Incorrect: Joanne and Todd's cars were bought from the same dealer; both proved useless, even though Joanne's car was an import and Todd's was a domestic model.

Correct: Joanne's and Todd's cars were bought from the same dealer; both proved useless, even though Joanne's car was an import and Todd's was a domestic model.