How to Normalize across multiple search results

I need some help in normalizing the score using Elastic Search. Before I proceed on to problem, some variables that are making an already difficult process even more difficult are discussed below. I use the following which can impact the process:-
1) N-Gram
2) Fuzziness
3) Custom Queries
4) Phonetic Search using custom filters
Now, my issue is say if I am doing search for 'Alice' and the best result is also 'Alice' with a score of 500, but for 'Cathy' whose best result is also 'Cathy' score is 200. If I take max score as the base to calculate for every other result, then also there is a problem. For example, let us say I searched for 'Hunan' for which best result is 'Rohan' with a score of 300. So the similarity score for 'Hunan' and 'Rohan' will be 100% even when they are hardly similar.
Moving on I am also trying to normalize score across searches, say search result with and without using phonetic search. If I can normalize the score for the two then I can stack them in an order of preference but otherwise I will have to show these results separetely.
Please let me know what I can do to resolve this issue.

Scores are not normalized in Elasticsearch, so I am not sure this this at all possible.

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