When using Participants Database Combo Multisearch, shows how to make the selections within a multiselect field work as OR terms when global filter mode is enabled.

pdb-multi-field-as-or.php

<?php
/**
 * Plugin Name: PDB Multi Field as OR in Filter Search
 * Description: make the selections within a multiselect field work as OR terms when 
 *              global filter mode is enabled
 */
add_filter( 'pdb-multisearch_filter_mode', 'xnau_set_multi_field_as_or', 10, 2 );

/**
 * sets the filter mode for the terms within a multi select field as an OR instead 
 * of AND when the global filter mode is enabled
 *
 * @param string $logic OR or AND if the global filter mode is enabled
 * @param string $fieldname the current field name
 * @return string must be "AND" or "OR"
 */
function xnau_set_multi_field_as_or( $logic, $fieldname )
{
  /* this assumes the name of the mult-select field you want treated 
   * as an OR is named "interests" so change that to match your field name
   */
  if ( $fieldname === 'interests' && $logic === 'AND' ) {
    $logic = "OR";
  }
  return $logic;
}

Selecting "OR"/"AND" could be a great extension to the "Combo Multisearch" plugin. Near the functionality of the filter from admin section "List Participants".