This example shows how to group several filters in the Members Directory of the Ultimate Member (with the custom table for usermeta).

um_grouped_filtes_custom.php

<?php

/**
 * This example shows how to group several filters in the Members Directory of the Ultimate Member. 
 * For example there are three phone fields in the profile ("Phone", "Phone number", "Mobile Number"), 
 * but you want to use a single filter "Phone number" to filter by these three fields in the Member Directory.
 *
 * Note: This example works if the setting "Enable custom table for usermeta" is turned on. 
 * See the gist https://gist.github.com/denisbaranov/3631abb45a05d6cdfbb6a4b6a6862b4c otherwise.
 * 
 * Change the variable $um_grouped_filtes. Add custom code to the file functions.php in the active theme directory.
 * 
 * Ultimate Member documentation: https://docs.ultimatemember.com
 */

add_filter( 'um_modify_sortby_parameter_meta', function( $sql_order ) {
	global $um_grouped_filtes, $wpdb;

	// Add your grouped filters here in a format 'main_filter' => [ 'additional_filter' ]
	$um_grouped_filtes = apply_filters( 'um_directory_grouped_filtes', array(
		'country'      => array( 'billing_country', 'shipping_country' ),
		'phone_number' => array( 'mobile_number', 'phone' )
	) );

	$md = UM()->member_directory();
	$directory_id = $md->get_directory_by_hash( $_POST['directory_id'] );
	$directory_data = UM()->query()->post_data( $directory_id );

	// filters
	if ( !empty( $md->custom_filters_in_query ) ) {
		$i = count( $md->custom_filters_in_query );
		foreach ( $md->custom_filters_in_query as $fk => $value ) {
			if ( empty( $um_grouped_filtes[$fk] ) ) {
				continue;
			}
			$grouped_keys = array_merge( $um_grouped_filtes[$fk], array( $fk ) );

			// JOIN
			foreach ( $um_grouped_filtes[$fk] as $metakey ) {
				$i++;
				$md->handle_filter_query( $directory_data, $metakey, $value, $i );
			}

			// WHERE
			$where = array();
			foreach ( $md->where_clauses as $j => $clause ) {
				foreach ( $grouped_keys as $key ) {
					if ( strpos( $clause, $key ) ) {
						$where[] = $clause;
						unset( $md->where_clauses[$j] );
					}
				}
			}
			$md->where_clauses[] = '((' . implode( ') OR (', $where ) . '))';
		}
	}

	return $sql_order;
}, 20, 2 );

Great work. Thanks for sharing. Exactly what I'm looking for. As I have a lot of filters I want to combine into one.

A question. Is this supposed to add to the fields 'mobile_number' and 'phone' to already existing 'phone_number' and then automatically work from the admin of filters? Or does one have to call the function from the code? If so how does one add it to the other filters that aren't grouped? Thankful for any advice :-)

You have questions about these code snippets in the UM Support Forum
https://wordpress.org/support/topic/merge-search-fields/

This gist is a part of the article Use a single control to filter by several fields in the members directory

Note: This solution is not recommended because it significantly slows down the directory. The relationship between the number of combined fields and slowdown is power-law: combining two fields slows down the search by two times, combining three fields - four times, four fields - eight times, and so on. It's better to use a general search line that searches by all fields.