In multisite, give editors and above the ability to upload whatever they want.

gistfile1.php

<?php

/**
 * Allow editors and above to upload whatever they want
 */
add_filter( 'map_meta_cap', function( $caps, $cap, $user_id ) {

	if ( 'unfiltered_upload' !== $cap ) {
		return $caps;
	}

	if ( user_can( $user_id, 'edit_others_posts' ) ) {
		if ( false !== ( $key = array_search( 'do_not_allow', $caps ) ) ) {
			unset( $caps[ $key ] );
		}
		$caps[] = 'unfiltered_upload';
		$caps = array_values( $caps );
	}

	return $caps;
}, 10, 3 );

/**
 * Allow editors and above to upload whatever, part two
 */
add_filter( 'user_has_cap', function( $allcaps, $caps ) {

	if ( ! in_array( 'unfiltered_upload', $caps ) ) {
		return $allcaps;
	}

	$allcaps['unfiltered_upload'] = true;

	return $allcaps;
}, 10, 4 );