You didn't say exactly what MP3 board you have (The VS1053 is the chip). If you have an SD card I assume it has enough memory for more songs, but you should know the size of the memory and the size of your files...
I assume the limitation is the lack of an operating system or a "proper" file system.
Can the Arduino directly read the MP3 files or anything from the SD card, or is it just directing/controlling the audio module?