Re:
Not to ruin anybody's party, but when paying somebody else for storage or putting bikes in boxes starts to make sense, then the line between enthusiast bike collector and just plain hoarder has been crossed.
I know it's easy to accumulate, and hard to reduce. I got to a point of having 10 bikes (although it was a rare occasion due to offering my father-in-law to fix and then sell all the old bikes he had in his basement). However, by end of the year I expect to be at 5, including the ones from my wife. And we'll see in 2016!
But if your problem is lack of space and the solution is to get additional storage, you are not tackling the cause (too many bikes) but rather the symptoms (basement full).
To reduce the number of bikes, I'd recommend to start slow. Pick your less favourite bike, fix it if it needs it, and then sell it. One of the best ways to realise how much real value our "treasures" have, is to put it on sale and see that people offer half of what we wanted. That is a painful but revealing wake-up call. To help with motivation, you could reinvest the money collected into the other existing bikes (upgrades, find that piece missing to complete one bike, build the spare frames, etc.). To me it was very gratifying how, with each bike sold, I was slowly reclaiming back my basement. More space to work on the remaining bikes, easier to find tools or spares, and also easier to pick whatever the bike from my stock I wanted to use at that moment (how many times you don't ride "x" bike because you need to remove another 5 to reach it?).
If all that doesn't work, you can always try:
-if your collection is really valuable and worth exhibiting, you can talk to your local authorities. In many cases, they have exhibition rooms empty, and might gladly host your bike collection if you offer to loan the bikes for free. Win-win for both.
-you could loan your less desirable ones to the friends/family you want to get into cycling. If they get hooked, they might buy your bike. If they don't, they are storing it for you on the meantime.
One more reason to make space in your basement. If you have no space left, you might have to pass on the next time you finally find that GREAT deal on a real classic...