They don't conflict; they were designed to work together. You can have schema.org (in JSON-LD, RDFa, or micro data) on the same page as Dublin Core, etc.

For example, there's no explicit property in schema's Person type [1] for a nickname. But the FOAF standard does [2].

Just add FOAF to the JSON-LD context:

    {
      "@context": {
        "@vocab": "https://schema.org/",
        "foaf": "http://xmlns.com/foaf/0.1/",
        "pronouns": "https://schema.org/pronouns" 
    }

    "@type": "Person",
      "givenName": "Timothy",
      "familyName": "Berners-Lee",
      "foaf:nick": "TBL",

[1]: https://schema.org/Person

[2]: https://xmlns.com/foaf/spec/#term_nick