I've been getting a lot of PMs about how I scored an interview at a great boutique in the city, especially with a soso
1. Cold call. It's a numbers game that is more about consistency than anything else I set aside an hour a day to call 5-8 firms. I would use google and make very targeted searches like "Mergers and Acquisitions NYC Boutique Healthcare" and then go through the results to find firms that are a fit. I was luck 2 positive responses out of 40 calls, a whopping 5% response rate, that's considered good, I was told to expect 1-2%.
2. Be consistent. The process isn't quick and it will take hours to figure out what your looking for, then to do the calls and make the contacts it's been over a month for me.
3. Know what you're going to say when you call. My script was "Hi, I'm XXXXXXXX and I'm calling regarding the possibility of an internship either this December or next summer?" This worked really well, if you're calling on a general number this usually gets you routed to the right person. Also it's to the point which helps.
4. Sell yourself. If you're nonbusiness, econ or finance this helps. Explain why you're a good fit and why you're switching course.