You could get multiple sites binding on either the capture or detection antibodies, which would affect the signal. However, as long as you have a reliable reference standard of the protein in question, such binding behavior will be controlled for.

My first guess would be the formation of di-sulphide bonds in your case. You can add some antioxidants like ascorbic acid in your buffer, try low pH for your protein buffer.

You can also try to reduce the protein with TCEP and then block the cysteines in your protein and then use it for ELISA.

Try to look for commercial kits for the protein you want to measure. Regardless if you buy them or not, finding one might give you hint about how to analyze your protein, native (polymeric) or if denaturing or other pretreatment is necessary. The kits often give you the rationale of the assay, even if they do not describe the exact composition of each reagent they do tell how they work.

Good luck 

Thanks @Brecher, @Triparti and Ramirez for your inputs.

As mentioned before, the oligomerization state will most likely influence your signal. The first point, what you have to clarify is, whether the oligomerization state varies in different samples. If not, then a simple calibration might be sufficient. If yes (this is more likely), you may have to dissociate your protein to monomers before you perform your assay.

I agree with Dr Tripathi, there will be indeed di-sulphide bonds. I would suggest you to see that whether this protein exists in multimer state under physiological state? If yes, I would suggest you to  do the elisa under  reduced state like Dr Tripathi suggested. But for functional assays and to determine its valency state and physiological relevance do your experiments under native condition.