We had this happen to us the year I joined 781. Here's a
thread about it.
Having two meetings in a row with high attendance doesn't necessarily mean much until the students stick around for any fall training/ activities that occur. This is usually when the high attrition rate occurs.
As for how to handle that large amount of students, it depends on four things: team infrastructure, team support to students, resources/facilities, and student interest.
1. how does your team's leadership look like? Do you guys have veteran students with defined roles or does everyone do a bit of everything? With these many students, you'll have a lot of work that needs to be handed out, and this will mean more people to hand that work out and make sure to teach new students how to accomplish their task.
2. How does your team support its students? Do your students have to pay for shirts/accommodations/transportation or is everything sponsored? Without extra sponsorship, I'd imagine that most of your students will likely need to pay to cover the costs of them being on the team. If this is not an option due to policies, financial support would need to be offered to deserving students.
3. Can your current facilities handle this large amount of students? Can everyone work in the shop at the same time without bumping elbows? While I can't imagine that much can be done about this on short notice if this is a problem, look in the area and/or ask the school whether it is possible for you guys to upgrading, citing the increasing student interest.
4. Does your team know what are the interests of these students? When 781 tripled in size four years ago, our administrative section saw the largest increase in students; do you have students interested in this business/ media side of FRC? This will give more roles for your students, although this may be an issue if your students all just want to build a robot. If this is the case, look into creating a VEX team (I have been out of touch with FIRST lately, but if my memory serves correctly, FTC is still not available in Canada).
Let me know if you have any questions via PM, I know the response I gave is rather vague without having a bit more information. I might also be able to help you guys out over the year in terms of mentorship, if required.