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<?php
add_filter( 'tgmsp_caption_output', 'tgm_soliloquy_custom_html', 10, 4 );
function tgm_soliloquy_custom_html( $html, $id, $image, $i ) {
    
    // If the ID doesn't match the one we want to modify, return the default HTML output. Change 324 to your slider ID.
    if ( '324' !== $id )
        return $html;
        
    // Append custom code output of the caption to do whatever. $i is the number of the slide.
    $html .= '<div class="my-custom-class"><p>My custom stuff!</p></div>';
    
    // Return the modified HTML output.
    return $html;
    
}