We had the same problem as you. The poles here were 28 mm, antique brass
colour (but made of steel), and 4m long. Originally they we just
supported near both ends, and by one bracket in the middle. The original
curtains were of thin, lightweight material, and really the poles were
fine for that.
We wanted to replace the curtains with very heavyweight curtains, and
the original brackets weren't up to the job. And we wanted a further
bracket, so that there were now four - one at each end, and one at 1/3
and 2/3 along the length. After a search around, we found there were
"open" type brackets and curtain rings. Examples here:
<
https://www.dunelm.com/product/pack-of-2-passover-brackets-1000000451?searchTerm=passover%20brackets>
<
https://www.dunelm.com/product/pack-of-6-unlined-passover-curtain-rings-dia-28mm-1000070273>
(We got our brackets and rings from Dunelm, but they were much heavier
duty than the ones in the links. I can't find the ones we used on that
website. You should find them on other websites, but they might be
called "passover", "bypass", or some other name.)
The other thing is that we were also concerned about possible sag in the
middle, so I put a 300mm length of dowel (actually an old broomstick
which was cut off!) in the centre of the curtain pole at the middle. It
was a good fit and we've not had any problems in well over 5 years.
--
Jeff