Then you need to redeclare in your current template (but better to create the new one and set this actions there) displayMsg method. It has the following code:

function displayMsg ($s, $bTranslate = false)

    {

        $sTitle = $bTranslate ? _t($s) : $s;

        $oTemplate = BxDolTemplate::getInstance();

        $oTemplate->setPageNameIndex (BX_PAGE_DEFAULT);

        $oTemplate->setPageHeader (_t('_Error'));

        $oTemplate->setPageContent ('page_main_code', DesignBoxContent(_t('_Error'), MsgBox($sTitle), BX_DB_PADDING_DEF));

        $oTemplate->getPageCode();

        exit;

    }

so to this part

$oTemplate->setPageContent ('page_main_code', DesignBoxContent(_t('_Error'), MsgBox($sTitle), BX_DB_PADDING_DEF));

can be transformed like

$sNewCode = $this->parseHtmlByName('your_custom_html_code.html');

$oTemplate->setPageContent ('page_main_code', $sNewCode . DesignBoxContent(_t('_Error'), MsgBox($sTitle), BX_DB_PADDING_DEF));

This redeclared method should be placed to the (for example) modules/boonex/protean/classes/BxProteanTemplate.php file

See the details about own templates here https://github.com/unaio/una-vendor-template

So, in this case, you will cover most cases about errors pages.