Answer:
You may be able to buy a condominium residence that has a basement.
Digging a basement under an existing condominium would require significant work on behalf of engineers, architects and so forth, in order to present a petition to the board for approval to dig a basement.
The board has the final say.
You can read your governing documents to determine the process for approval for modifying your unit. Modifying other than your unit might not be an option.