Saxon

This whole area is certainly delicate and fragile.

I think that in general, Receiver.setSystemId() must be called before startDocument(), and it applies to the document as a whole. To set different base URIs on different elements, the mechanism is to supply this in the location property on the startElement call. But it seems that setSystemId() is needed at the document level as well. The following seems to work after a fashion:

        Receiver receiver = destination.getReceiver(pipe, new SerializationProperties());
        try {
            receiver.setSystemId("http://example.com/");
            receiver.open();
            receiver.startDocument(0);
            FingerprintedQName wrapper = new FingerprintedQName("", "", "wrapper");
            Location loc = new Loc("http://example.com/", -1, -1);
            receiver.startElement(wrapper, doc.getUnderlyingNode().getSchemaType(), EmptyAttributeMap.getInstance(),
                                  doc.getUnderlyingNode().getAllNamespaces(), loc, 0);
            while (iter.hasNext()) {
                XdmNode node = iter.next();
                if (node.getNodeKind() == XdmNodeKind.ELEMENT) {
                    loc = new Loc("http://bar.com/", -1, -1);
                    receiver.append(node.getUnderlyingNode(), loc, 0);
                } else {
                    receiver.append(node.getUnderlyingNode());
                }
            }
            receiver.endElement();
            receiver.endDocument();
            receiver.close();

Note also that setting the base URI didn't work on the text node. I'm not sure it matters but it would matter if that didn't work on a processing instruction.