Limit Upload Count per User Role

Hello,
I’m trying to create a multi vendor marketplace. I would like to limit upload file count to 3 per session.

I could not find such a code there were only examples about limiting upload sizes. Should I need to change core files? I just need to disable multiple file upload feature or limit it with max 3.

By the way there was one example but it counts all uploads by user. I want it to count per session.

add_filter( 'wp_handle_upload_prefilter', 'wp_check_upload_limits' );
function wp_check_upload_limits( $file ) {
    $current_user = wp_get_current_user();
    $current_user_role = $current_user->roles[0];

    if ( $current_user_role != "contributor" )
        return false;

    $upload_count = get_user_meta( $current_user->ID, 'upload_count', true );
    $upload_count_limit_reached = apply_filters( 'wpse47580_upload_count_limit_reached', 100 ) > ( $upload_count + 1 );

    if ( $upload_count_limit_reached )
        $file['error'] = 'Upload limit has been reached for this user!';

    return $file;
}

Thank you.
Best Regards.