Upgrading 10 Speed Groupset

You don't mention your objective from upgrading.

Over the past few years I have upgraded the majority of components on my 10 speed group set bike except the cranks, front derailleur and shifters. It has made the bike more comfortable and more enjoyable. When I added up the cost, I have spent over 70% of the original bike price doing this. I learnt a lot about what I want from a bike which helped me justify buying a much more expensive 11 speed goupset bike last year.

I would suggest you ride and enjoy your bike, upgrading parts with those objectives front and center.

Assuming you have double rather than triple chainring, and a fairly recent Tiagra mech, then you would need one 11 speed shifter, chain and cassette. The rear mech will be fine with an 11 speed shifter. The front mech and shifter could stay. If you are changing cassette and chain, it would make sense to put new chainrings on - not because your existing ones are incompatible, but because they will be worn.

The bigger decision to make is about gearing. Going to 11 speed can give you the same range with smaller gaps, or a wider range between highest and lowest. Everyone has their opinions on this - some will claim you are not worthy to have an 11 tooth on the back, because who needs to go fast downhill? I live in a hilly area, and like to make it up without my knees exploding, and down as fast as I can. For that I'm looking at an XD freehub, and a 9 to x cassette, where x is as big as the range of the mech will handle. Then a subcompact chainring to get the low gears. If you ride in a flat area, you might choose differently.

it could be that a change like that is beyond them to do, or they think it's uneconomic. I think it's marginal - depends how much you like the rest of the bike, how old it is, and what else, if anything, you own. 

It's an all/nothing commitment to change up to 11 sp. The new cassette is just the start, as you've noted.  Curiously enough, it's not like the bottom has dropped out of the 10s market, prices wise.

An alternative might be stick on 10s (I only run one 11 sp Ultegra bike everything else is 10s or vintage). You've probably got an FSA chainset, so consider changing that, the chain and the sprockets - you can still get good 10s stuff. If your brifters are old and well used, they will eventually die - but they are an expensive item and effectively cement you in to that number of gears.

I run brifters on several bikes, but you could consider having down tube /friction levers if you've got the bosses, or band-on if you're running a steel frame. They work fine. 

As per others, much better to spend your money on better wheels (or a saddle that really suits you, the best investment of all)! Three bikes ago I had Tiagra 10 speed and I thought it was great, I then bought another with 105 10 speed and couldn't see much difference, then Ultegra mechanical 11 speed, still couldn't see much difference, now I have Ultegra 10 speed Di2 and although I love the Di2 element I don't miss having an extra gear. I have come to realise (ably assisted by my dear wife's comments) that most of my upgrades have been more driven by a desire to have a spiffy name on my groupset than any genuine advantage. Last year the great Harry Tanfield said to me in a FB discussion that Dura Ace really just wasn't worth the money compared to Ultegra...when mates ask me now what they should be looking for in a new bike I tend towards 105 or Tiagra being all you'll need unless you're really going in for serious, must save 200 grams racing.

It's totally possible, if you're prepared to buy shifters, rear mech, chain and cassette. Is it worth it? That's a question only you can answer. I might keep an eye on Ebay for a sensibly priced 105 or similar; they do come up every now and again. I'm guessing you're running rim brakes; if so, those groupsets can be had 2nd hand fairly cheap these days. 

I've got to agree with Joe Totale, I actually run Tiagra on my summer bike and Ultegra on my winter bike.

Ultegra is definitely crisper but I wouldn't say it's so much better to be worth the cost of an after market upgrade.

One thing to consider is getting a cassette that has a 12 tooth smallest cog, you then essentially have the same gears as 11 speed but without the 11 tooth cog which you likely use least of all anyway. Far cheaper upgrade than a whole gruppo.

Use the money saved to get a nice set of alloy wheels and some top of the range tyres and your bike will feel so much better and likely be lighter than if you just did the groupset.

Check that the crank is 11 speed compatible (it should be). Also don't forget an 11 speed cassette. 

So basically, if you're happy to buy a most of/a full 11 speed groupset then there's no reason why you couldn't upgrade to 11 speed. 

What I would say though is that are you sure all the extra expense is worth it for 1 additional gear? I've used both a lot and Tiagra is pretty good stuff, Ultegra is a bit better but I'm not sure it's several hundred pounds better. Tyres and wheels would be a more cost effective upgrade in my view.