This is for sure the way to go.
A couple of details:
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Items returned are not unique. I see "Armani" is in the first and in the second result set. Is there a way to avoid duplicated results ?
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I see you specified the "size": 5 in the last query but I don't have this parameter. I want a maximum of 10 items from the first query and a maximum of 5 from the second one and 20 results in total. This means that if the first query returns 3 items (because there aren't other items that match the query) the second one return 5 I want the third one to return 12 items (20 - (3+5))