How can a money-transfer startup scale and enter additional countries?

You can do this in many ways (depending on how much time and money you have on your hands):

• You can start writing to the specific department that deals with Inward Remittances in each Central Bank of the country you are interested working with. Ask them to provide you with working banks to tie-up with. The downside is, you may end up with a bank, MSB, etc. that may not be an ideal partner.
• You can visit various Money Transfer related conferences / trade shows in the region
• You can write to the Commercial Counsellor at the Embassy in your country, for the country you want to work in.
• You can hire/work with specialised companies who do this for a living, provide remittance tie-ups and handle the entire process as a turn-key project.
• You can write to the financial regulator and obtain a list of all qualified (read: licensed) MSBs, Banks, etc. who are authorised to handle incoming foreign exchange money transfers. The downside is the list itself (who do you trust? who is a big player? who is the right player).
• You can start by advertising on Google in the country of interest