Optimising the sorting of the array that uses compound comparator and limit

I have a task of sorting an array of restaurants there are multiple fields they are ought to be sorted by. [open/closed,building number, distance, relevance]
My issue is that in order to evaluate the distance metric I need to send a request to the specific api. I also need to minimize the number of requests sent. But here is the caveat I only need 10 values from the top of the sorted list. And this made me think that I might not need to send the request to evaluate the distance for all of the restaurants if for example after sorting the list by open/closed the number of restaurants in the first group is larger then 10 I do not need to sort the remaining restaurant by their distance, same applies for the building number in this example.
My question is - is there a way to do this elegantly in Java, or will I have to write my own stuff.

First, sort by all of the fields that are cheap to sort by (ie you don't have to call the external API). With best first.

Next build a Priority Queue with a comparator that works exactly like you want but returns the worst element first. Have it also cache results from calling the API so that you don't call twice for the same element.

Put the first 10 of your sorted list into your queue.

Go through the rest of your list. If it is better than the minimum in your queue, add it to the queue and pop from the queue. If it isn't, then just move to the next.

Once you are done, your priority queue has the 10 best. It will give them to you from worst to best. So pop 10 times then reverse the array for your final answer.

This will run the expensive lookup only when you have good reason to believe that it will be in the final answer, and when this lookup is required to break a tie.