AvalonBay Communities Inc. is proposing to significantly increase the number of residences in a 40-story complex it wants to build next to the TD Garden.

The developer filed documents this week with the Boston Redevelopment Authority outlining its new plan for the property, which is situated on air rights above an MBTA Parking garage off Nashua Street. A previously approved plan called for 363 residences, but AvalonBay’s amended proposal now calls for 500.

The latest plan does not increase the height of the tower, but calls for a more densely packed building to accommodate about 140 additional residential units. It would also reduce the number of parking spaces from 270 to 219.

AvalonBay indicated in its filing that its has not decided whether the units will be rental apartments or condominiums.

The company is taking over management of the project from its prior developer, the Boston Garden Development Corp., which initially filed plans for a large residential complex in 2004. It later revised the plan in 2005 and received final approval from the city in 2006.

But construction never moved forward and the economy deteriorated in 2007, leading to a building slump that has only recently ended. Several large residential projects are moving forward around the Garden, including a 186-unit building now rising along Causeway Street over the O’Neill tunnel.

“We are very excited about moving forward with this project and look forward to working with you, your staff, elected officials, community members and the impact advisory group,” Avalon wrote in a letter to BRA director Peter Meade.

The BRA’s approval is needed before the project can proceed. Avalon has not said when it wants to start construction.