Михаил

$array = [
    0 => ['a' => 1, 'b' => 2, 'c' => 3],
    1 => ['a' => 1, 'b' => 3, 'c' => 3],
    2 => ['a' => 1, 'b' => 2, 'c' => 4],
    3 => ['a' => 1, 'b' => 2, 'c' => 3],
];

$keys = array_keys($array[0]);

$keys = array_filter(
    $keys,
    function($key) use($array) {
        count(array_unique(array_column($array, $key);)) > 1;
    }
);

$array = array_map(
    function($el) use($keys) {
        return array_filter(
            $el,
            function($key) use($keys) {
                return in_array($key, $keys);
            },
            ARRAY_FILTER_USE_KEY
        );
    },
    $array
);

print_r($array);

/*
Array (
  [0] => Array (
    [b] => 2
    [c] => 3
  )
  [1] => Array (
    [b] => 3
    [c] => 3
  )
  [2] => Array (
    [b] => 2
    [c] => 4
  )
  [3] => Array (
    [b] => 2
    [c] => 3
  )
)
/*