For streaming protocols such as TCP, you can pretty much set your buffer to any size. That said, common values that are powers of 2 such as 4096 or 8192 are recommended.
If there is more data then what your buffer, it will simply be saved in the kernel for your next call to recv.
Yes, you can keep growing your buffer. You can do a recv into the middle of the buffer starting at offset idx, you would do:
recv(socket, recv_buffer + idx, recv_buffer_size - idx, 0);