下面是使用Python实现的一种解决方法：

def nested_sort(arr, keys):
    if len(keys) == 0:
        return arr
    
    key = keys[0]
    arr.sort(key=lambda x: x[key])
    
    for i in range(len(arr)):
        if i > 0 and arr[i][key] == arr[i-1][key]:
            sub_arr = [arr[i-1], arr[i]]
            
            j = i+1
            while j < len(arr) and arr[j][key] == arr[i][key]:
                sub_arr.append(arr[j])
                j += 1
            
            sorted_sub_arr = nested_sort(sub_arr, keys[1:])
            
            arr[i-1:i+j-1] = sorted_sub_arr
            i += len(sorted_sub_arr) - 1
    
    return arr

使用示例：

arr = [{"name": "John", "age": 25, "score": 80},
       {"name": "Alice", "age": 23, "score": 85},
       {"name": "Bob", "age": 25, "score": 70},
       {"name": "Alice", "age": 22, "score": 90},
       {"name": "John", "age": 20, "score": 75}]

keys = ["name", "age", "score"]
sorted_arr = nested_sort(arr, keys)

for item in sorted_arr:
    print(item)

输出结果：

{'name': 'Alice', 'age': 22, 'score': 90}
{'name': 'Alice', 'age': 23, 'score': 85}
{'name': 'Bob', 'age': 25, 'score': 70}
{'name': 'John', 'age': 20, 'score': 75}
{'name': 'John', 'age': 25, 'score': 80}

这个方法通过递归地对每一层嵌套键进行排序，保持其他层级的排序不变。