How to activate polystyrene with carboxyl group?
It is certainly possible to nitrate polystyrene powder with nitric &amp; sulfuric acid mixture and reduce the nitro groups to aniline with $\ce{SnCl2/HCl}$ as described in here1. How effective this would be for a microtitre plate I cannot say, but chemistry is an experimental subject.
Reference

Zhao, H. &amp; Guo, J. &amp; Bian, L. &amp; Wei, Z. &amp; Deng, K.. (2009). Synthesis of nitro and amino linear polystyrene. Hecheng Shuzhi Ji Suliao/China Synthetic Resin and Plastics. 26. 22-26. (link)