How to use match_phrase and fuzzy query at the same time

I'd like to search documents by phrases and do not need to match all the words included in the phrases, but only some (specified) words / characters. For example,

{
  "match_phrase": {
    "target_field": {
      "query": "This is the phrase"
    }
  }
}

I do not need exactly match This is the phrase, but also want to get documents only with is the phrase or This is the phras.

Is there any ways to add some fuzziness to match_phrase query like this?

My question is very similar to this (Match_phrase + fuzziness query porting from ES 1.7.x to ES 7.1.x), but there are no answers yet.
Also I do not want to use span queries because the query will be very long.

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