There are two solutions:
1. JQuery
<div id="stuff-from-other-side"></div>
<script>
$.get("<%inf_custom_variant_current_page_url%>", function(data){
$("#stuff-from-other-side").append(data);
});
</script>
2. Server side include that runs onced published to the web server
ASP Code:
<div id="stuff-from-other-side">
<!--#include file="<%inf_custom_variant_current_page_url%>"-->
</div>
Please note that <%inf_custom_variant_current_page_url%> is an info
placeholder with setting of current page url and project variant of
custom.
-Jian