Hawksmoor's third enlargement scheme is the best documented and most detailed of his three proposals for extending the hospital in 1711. It is the only fully worked out enlargement scheme and, after several revisions, was still on Hawksmoor's drawing board in 1728, when he had two versions of the plan, with and without the chapel (RIBA SA 70/4; former E5/9; Hart 2002, fig. 302; and SA 70/6; former E5/11; Bold 2000, fig.144; a version of the latter was engraved, see Wren Society, VI, pl. 15).

In the 1711 version of the scheme the Queen's House is retained, extended and refronted, and the chapel and road are moved northwards, to a position roughly halfway between the Queen's House and the hospital; see [9/1]. The chapel is now a square-plan, domed, peripteral building, 180 feet wide (the width of the the chapel in the park in the first enlargement scheme; [6/1]). It is entered from the north side, towards the river, and is connected to the two south dormitories by arcades that join the northernmost intercolumniations of the two side colonnades of the peristyle and turn through right angles to join the centres of the two south dormitories. The relationship of chapel to hospital, in plan and perspective, is illustrated in the pencil sketches on the earliest known design for the scheme at [9/1].

There is no direct road access from the west side. The chapel now serves the hospital only. The altar is on the south rather than the east side of the interior and the road passes beneath the middle of the chapel.

The scheme can be dated to the summer of 1711 on the basis on an inscription on the back of the final plan at Worcester College: Greenwich. Aug.^t 9.^th anno 1711 (Colvin 1964, cat. no. 60; Wren Society, VI, plate 40, top left). Two other drawings are also inscribed 1711: a presentation design at Worcester College for re-fronting the Queen's House as a three-storey building (Colvin 1964, cat. no. 62; Wren Society, VI, plate 40, top left), and a west elevation of the chapel and courtyard in the Courtauld Insitute of Art Gallery Collections (DD.1962.XX.2.8; Wren Society, VI, p. 92, lower). This last drawing shows the 20-feet drop in level between the ground at the base of the chapel and the ground on the south side of the main hospital courts. It shows the courtyard elevation of the arcade on the east side. It is 11 bays long, including the bay which aligns with the north colonnade of the chapel. The area of lower ground is 60 feet wide and has three bays of arcade set on a rusticated lower arcade. It is clear from this drawing that there was no access to the chapel from Greenwich itself other than through the main hospital courts.

The most detailed plan of the scheme is Hawksmoor's drawing at the RIBA inscribed at the bottom, The Royall Hospitall at Greenwich 1728 N.H. (RIBA Catalogue, Hawksmoor [1]/2; SA 70/4; former E5/9; see Hart 2002, fig. 302). The RIBA plan drawing is an adaptation of an earlier design for the revised first enlargement scheme, for it has a plan of the rectangular chapel of that scheme concealed beneath the pasted overlay that bears the plan of the new chapel and court. The plan shows the arcades meeting the central doors of the two south dormitories and returning to connect with the ends of the colonnades.