Plasma samples may "clot" out on you during the ELISA process and
"capture" all kinds of crud.
Try the same procedure with a serum sample - if better background, then
you have a partial answer.
Also, perform a short experiment to see WHERE the BG signal comes from
(is it the sample, is it the primary antibody, is it the secondary, is
it the blocking reagent) - this experiment is best done by running a
know positive and negative sample and leaving out the "crucial"
component (the primary, the secondary etc.) - then sit down and look at
your results and you will be far ahead!
Switching to a high sensitivity substrate will often allow you much
higher dilution of the enzyme conjugate, thereby usually eliminating
most/all background - I think chemiluminescence is the highest
sensitivity currently.