Yes, visitors can apply for an Extension of Stay to extend their visit to The Bahamas.

An extension on visitors’ stay may be granted to applicants who qualify. All visitors applying for an extension of stay must present themselves in person to the extension officer, accompanied by their sponsor and all required documentation.

To be considered for a visitor’s extension, applicant must provide the following to the extension officer:

• Proof of Payment (options include credit/debit card, bank draft, or Bahamas Postal Money Order)
• Return ticket or Temporary Cruising Permit
• Valid Passport
• Local Address
• The Immigration Landing Card
• Provide Reason for Extension of Stay
• Evidence of Bahamian Visa if applicable
• Valid Email Address
• Mobile Telephone Number
• Sponsor’s Passport and Address

More information can be found here