17
Both are acceptable but mean slightly different things. "To make a space" implies that a specific open area is being made for a specific purpose or object in a particular location. "To make space" is more vague and relaxed and denotes the creation of more available space in general. In some cases one is more appropriate than the other, and in other cases both would work. As a native speaker my ear has a preference for "to make space" so I'd prefer that form if there is overlap.
10
I think it is probably more idiomatic to use:
make room (for someone or something):
to provide space for someone or something.
- Make room for Sam. He needs a place to sit. Can you make room for this package?
(The Free Dictionary)
See also Google Books for make room, vs make space, make a space.
9There is an implication of discreteness. 'A space' implies they are countable, like chairs or desks or parking spaces or something. 'Space' implies continuous space which isn't being counted, like in a park or on the ocean. – user1908704 – 2018-09-12T21:06:00.473
1Also, "make a space" could imply that there currently isn't any space, while "make space" could imply adding more space to an existing space. – jaxad0127 – 2018-09-12T22:38:21.457
This is correct. Another way to think of it is to view "to make space" as a short version of "to make some space". – BradC – 2018-09-13T14:23:10.123
We usually say: "make some space", for a specific item. eg: Could you make some space for my rocking chair? – Vic – 2018-09-24T10:31:45.477