Just as in English nouns in French can be mass nouns, countable nouns and other sorts. In this particular case the English syntax is the same, as “room” is uncountable as well as “place” in French; so, you can’t have a plural as it is a mark of countable nouns; once you understand that you must keep in mind that the syntax differs in the way that the adverb is connected to the mass noun; for that part of the question see this answer and this other one (partitifs indéfinis).