Proposals have emerged for a new high-rise building next to Guy's Hospital in St Thomas Street at London Bridge, just across the road from the Shard.
Now the company has revealed it is planning a very tall building on the site, potentially more than trebling the existing office floor space of 98,500 sq ft.
At a recent presentation to investors, portfolio director Neil Thompson said that New City Court represented "an exceptional opportunity to build a cutting-edge building benefitting from the regeneration and market repositioning of London Bridge".
He added that "early meetings with the planners suggest that a building of up to 300,000 sq ft may be possible".
By comparison, GPE's recently completed 20-storey development at 240 Blackfriars Road is 235,000 sq ft.
New City Court's tenants currently include The Body Shop, PR firm Four Communications and Guy's and St Thomas' NHS Foundation Trust.
GPE is also working on plans for a more modest redevelopment of Minerva House next to Southwark Cathedral where, according to Thompson, the company proposes a "high calibre river-fronting mixed-use development of around 120,000 sq ft up from 97,000 sq ft today".
Minerva House was acquired by GPE for £60 million at the end of 2012.