Once inside the basilica how and where does one purchase a ticket for the towers?
It's to the left after you enter the church but it was sold out when I tried to buy tix as it's very popular. There's an option on the website to buy tower tickets in combination with entry. That's the only option.
Tim, it's not as simple as getting "an extension" on the spot. You might find out that you can't go up the towers that day if the tickets have sold out. There's a number of max visitors (Health and Safety regulations). Besides, even if you could, queuing on-site can be a nightmare depending on the day you're visiting due to the sheer number of visitors. Your best bet is to email them a.s.a.p., explain the situation and ask for a change of tickets. In most cases, the support staff is very accommodating and will surely help you to change your purchase. Good luck. Btw, I suppose you know, but the official page is www.sagradafamilia.cat