Bob, Sone
I have an EU passport, so the rules are different for me, but my gf is an "undesirable" from a poor country and we've been struggling with this recently so I've also done a lot of research. A few replies to Bob's points:
1 - Going out and coming back works just fine if you're on a visa-waiver. I've met Americanos who have managed to stay in Europe for years and years by bouncing between the Schengen zone and non-Schengen countries. (UK, Ireland, Cyprus, beautiful Bulgaria, etc.)
But if you require a visa, surrounding countries usually use that one as the reference point. While you have a still-VALID Schengen visa, you can spend a week or two in Serbia, or up to 90 days in Bulgaria, for example, without any other kind of visa. But when your Schengen visa expires, they won't let you into those countries either. We're in Turkey right now for exactly this reason. We couldn't get a visa for Bulgaria after the Schengen visa expired. Europe doesn't like people from poor countries to keep coming back, and if Sonje's on a Namibian passport she will probably have the same problem.
Turkey has a separate visa regime, and it's relatively easy to extend visas once you're there. It's also a fascinating place, so Sone could feasibly spend three months travelling across Europe to Istanbul and then three months in Turkey.
BUT, something I just remembered, is that in many cases you have to apply for your Shangen visa from the country where you are resident. If you're just hanging out in Ireland, you may not be able to apply for a visa from there. You may have to establish residency first. Establishing residency temporarily in Turkey seems to be easier, but there is still no guarantee of getting a visa. Like I said, they don't want people from poor countries applying for multiple visas.
Overstaying is a very messy issue. I know one guy (American) who was barred from re-entering the Schengen zone for a year because he crossed the border from Greece three hours after midnight on his last permitted day. Three hours overstay and huge trouble. On the other hand, I crossed the exact same border with my girlfriend and nobody checked her passport. She didn't get a stamp, and that created problems later on. The border police suspected she was overstaying when in fact we had been very careful to stay within the limits. One of her friends had a similar problem because he entered France from the UK on the train and nobody stamped his passport. My advice is to be very careful to BE SEEN to be following the rules. Make sure you get stamped.
2 - The tourist visa specifically states on the application form that no extension will be granted, except for verified medical emergency. Even if you meet and marry a local, you still have to leave and apply for your residence permit from your country of residence. Americans on a visa-waiver can apply for residence in certain countries, depending on circumstances, while they are there, but anyone requiring a visa is out of luck.
3 - Establishing residency is difficult if you're not bringing lots of money with you. The easiest option for Sone would probably be to enrol on a language course in one country and then travel wherever she wants. But, depending on the country, there is probably a requirement to actually go to the classes. A year in Spain or France, with trips to other countries, is not a bad option so I wouldn't discount it if you can afford it.
In conclusion, I would still recommend trying to get a long-term multi-entry visa. You'll need to do your own research about where to apply from, as each embassy will have different guidelines and you may need to be resident in whichever place you apply from. Then put together a travel schedule that will make sense to the people processing the application. eg three months in northern Europe, three months in Ireland, three months in Spain and North Africa, then via Italy to Eastern Europe, going out of Schengen to Bulgaria, Turkey, then back to Schengen via Greece.
The exact route is not important, but it should justify giving you a multi-entry one year visa. You will still be subject to the 90-day rule, so your schedule should make sense from that perspective, but will be able to go in and out.
Also, I don't know if you (Sone) have looked at the application form yet, but for my girlfriend we had to supply confirmation of accomodation bookings for the entire travel plan as well as show money in the bank. I had quite an argument with the guy at the embassy because the visa didn't allow for the possibility that plans might change. You can't even build gaps into your plan in case you decide to stay a few days extra in one place, or make side-trips. Stuff like couchsurfing doesn't count, it has to be at a proper hotel or hostel, or a legally rented apartment.