There are many ELISA's optimized for Plasma/Serum both single and multiplex. You can also use flow based cytokine kits that are multiplex. The Luminex platform is also used often if you have access to a compatible machine and multiplexes for very large panels. Just confirm on the vendor site it will work for plasma/serum prior to purchasing.
As William Suslovic said, you could use single/multiple antigen ELISAs or multiplex bead based technologies. Single antigen ELISAs are easier to perform and all you need is a plate reader that can measure absorbance. Some of the multiplex ELISAs can also be done using a plate reader. Bead based techniques like CBA or Luminex would need access to specialized equipment like flow cytometers or luminex instrument.
May I suggest Ella by Simple Plex. An automated ELISA. Helps in avoiding operating factor that might affect the final measurement, faster results, and more economical if compared with ELISA kits.