DXB is in Europe (at least for the purposes of this ticket) so once you leave Europe (and go to HKG, which is in Asia), you can't go back to Europe. If you want to do any extra segments in Europe, you have to do them before you leave the continent (on this ticket).

I thought I just realized that I had suggested an invalid routing earlier - that is, DFW-LHR-IST /cruise/ DXB-LHR //home on separate ticket // HEL-CDG-NRT. That's 5 segments in Europe (LHR-IST-DXB-LHR-HEL-CDG) and you're only allowed 4 - however, it's only 4 flight segments (because IST-DXB is a surface segment) so it is, in fact, ok. The IST-DXB surface segment counts against the total 16 segments you're allowed but doesn't count against the maximum of 4 you're allowed in Europe. I think that's correct - if not, someone will very quickly correct me!

I had suggested HEL in that routing because - apart from Helsinki being an interesting city, worth a day or two to visit - as Finnair's hub, it has a lot of connections to other places in Europe (basically anywhere Finnair flies, obviously). Only downside to Finnair is they don't have F on their longhaul flights (or in Europe, but then nobody does in Europe on the shorthaul flights - it's like 'F' on AA in the US). From Helsinki, you can take the ferry across the Gulf of Finland to Tallinn in Estonia - we haven't done that (yet) but Tallinn seems to get high marks from those that have. If you're interested -

http://wikitravel.org/en/Tallin

If you do LHR-IST//DXB-LHR as 2 of the 4 permitted flight segments in Europe, you could also just go somewhere else in Europe (Barcelona? Vienna? Prague?) and then back to LHR, before leaving for Asia. If you do a separate ticket from LHR to get you back to DFW (and then return to LHR later to continue the ticket), you can obviously do those 2 extra segments in Europe either before or after you return to the US (on the separate ticket). As I said before, the possibilities are endless, constrained only by the time and funds available.