The members of Central Fife Licensing Board agreed to the move after hearing the case for Blue Monday at their meeting last week.
The 80s bar was also seeking an entertainment licence for live and recorded music, dancing, bands and cabaret, opening until two in the morning.
Their proposal involved creating an exit to the rear of the premises, taking people away from the High Street and into the service area. However Fife Police had reservations.
"We are concerned about people exiting into the back area and the nature of the steps they would be using which are concrete and steep and with poor railings," Superintendent Alan McIlravie said.
"This is also a relatively dark area and we would need to have assurances of lighting and CCTV.
"It also has to be remembered that this is a business area and not designed for pedestrians so there are concerns about safety as this area is used by young people turning in their vehicles.
"In addition, this area already serves three late night establishments and putting more people in could lead to problems."
Kirkcaldy West Community Council also raised objections on grounds of over provision, public order and disturbance.
"These premises are adjacent to other similar places and we submit that this will be one too many," a spokesman said. "We are only objecting to the extension which we do not think is necessary."
Objections were also received by neighbouring establishments regarding too much competition but the agent for the owners of Blue Monday dismissed these claims and the other concerns raised.
"These premises are already licensed, the police are aware of their suitability and a planning certificate for this proposal was granted recently," he said.
"The physical problems have been dealt with - the staircase at the rear will be covered, with a steward at the top and bottom.
"Police resources are also not a valid reason for rejection but even so, surely exiting at the back solves a problem as it seems eminently sensible to take people out to where the police and taxis already are.
"My clients run good premises, the only bar of its type in the town, and will continue to do so with regard to residents and its customers."
The licensing board agreed to visit the premises and the back area at night and deferred the matter to the adjourned board in November.
A similar application for an extension and entertainment licence from Bar None was also adjourned.