Right - once the monomer is reacted, all you have is a long alkane chain with pendant benzene rings. To have any chance of reacting with the polymer, you need a reaction that occurs on a weakly substituted (alkyl) benzene ring, on the activated α-carbon, or on the alkane chain. There aren't many clean possibilities. You could look at electrophilic aromatic substitution reactions - you probably don't need to react every single benzene ring so even low yield reactions, if they are clean, should be effective.
Usually if you really need particular functional groups in a polymer, it is easier to incorporate them into the monomer before the polymerization reaction. If you're trying to use commercial products, that's probably not available.
For commercial products, of course, you will also have to worry about contamination from plasticizers and co-monomers the manufacturer uses to adjust the properties of the polymer. It's hard to tell what those are without specific information from the manufacturer.