Source

File: wp-includes/class-wp-theme.php

public static function get_allowed_on_site( $blog_id = null ) {
		static $allowed_themes = array();

		if ( ! $blog_id || ! is_multisite() ) {
			$blog_id = get_current_blog_id();
		}

		if ( isset( $allowed_themes[ $blog_id ] ) ) {
			/**
			 * Filters the array of themes allowed on the site.
			 *
			 * @since 4.5.0
			 *
			 * @param string[] $allowed_themes An array of theme stylesheet names.
			 * @param int      $blog_id        ID of the site. Defaults to current site.
			 */
			return (array) apply_filters( 'site_allowed_themes', $allowed_themes[ $blog_id ], $blog_id );
		}

		$current = get_current_blog_id() == $blog_id;

		if ( $current ) {
			$allowed_themes[ $blog_id ] = get_option( 'allowedthemes' );
		} else {
			switch_to_blog( $blog_id );
			$allowed_themes[ $blog_id ] = get_option( 'allowedthemes' );
			restore_current_blog();
		}

		// This is all super old MU back compat joy.
		// 'allowedthemes' keys things by stylesheet. 'allowed_themes' keyed things by name.
		if ( false === $allowed_themes[ $blog_id ] ) {
			if ( $current ) {
				$allowed_themes[ $blog_id ] = get_option( 'allowed_themes' );
			} else {
				switch_to_blog( $blog_id );
				$allowed_themes[ $blog_id ] = get_option( 'allowed_themes' );
				restore_current_blog();
			}

			if ( ! is_array( $allowed_themes[ $blog_id ] ) || empty( $allowed_themes[ $blog_id ] ) ) {
				$allowed_themes[ $blog_id ] = array();
			} else {
				$converted = array();
				$themes    = wp_get_themes();
				foreach ( $themes as $stylesheet => $theme_data ) {
					if ( isset( $allowed_themes[ $blog_id ][ $theme_data->get( 'Name' ) ] ) ) {
						$converted[ $stylesheet ] = true;
					}
				}
				$allowed_themes[ $blog_id ] = $converted;
			}
			// Set the option so we never have to go through this pain again.
			if ( is_admin() && $allowed_themes[ $blog_id ] ) {
				if ( $current ) {
					update_option( 'allowedthemes', $allowed_themes[ $blog_id ] );
					delete_option( 'allowed_themes' );
				} else {
					switch_to_blog( $blog_id );
					update_option( 'allowedthemes', $allowed_themes[ $blog_id ] );
					delete_option( 'allowed_themes' );
					restore_current_blog();
				}
			}
		}

		/** This filter is documented in wp-includes/class-wp-theme.php */
		return (array) apply_filters( 'site_allowed_themes', $allowed_themes[ $blog_id ], $blog_id );
	}