I'm planning a model of a line that is similar to this idea, but not entirely the same.
The Gwash Valley Railway (GVR) was first opened in 1867, running from Oakham to Empingham. The company intended to extend the line to join the Stamford and Essendine Railway at Ryhall, doing so in 1871. This extension provided access for Mid Rutland farmers to the GNR's East Coast Main Line. However, it put the GVR at odds with the Midland Railway, who had previously authorised the company to use their station. The MR demanded that the GVR open their own station at Oakham and dismantle the connection to the MR's metals. Running powers over the S&ER were granted to the GVR in the same year and a spur was later constructed near Ryhall to allow trains from the GVR to run south to Stamford East.
The assent of the GN&LNWJR in 1874, drew the attention of the GVR; who, in 1875, chose to amalgamate with the S&ER to form the Leicester, Peterborough and East Coast Railway. The new company planned to create a new middle-distance route between the two cities; to rival the MR's line and connect with the Peterborough, Wisbech and Sutton Bridge Railway so as to reach the new dock at Sutton Bridge (which had been given assent in 1875). The newly formed LP&ECR proposed two extensions in 1876, one from Oakham to the GN&LNWJR at Tilton, which would provide the railway access to the Great Northern Railway's Leicester Belgrave Road branch; and another from a junction at Sutton on the former S&ER's Sibson Extension, to connect with the Peterborough Wisbech and Sutton Bridge Railway north of Peterborough. Of the two schemes, only the Leicester Peterborough and East Coast Railway (Western Extension) was successful and reached Tilton in 1879. The eastern extension however, failed, having been blocked by Earl Fitzwilliam of Milton Hall. Running powers were granted to the L&PJR over the Leicester Belgrave Road branch and the Northampton and Peterborough Railway by the GNR and LNWR respectively.
Like the GNR, in 1876, the LP&ECR also gave its support to the ill-fated Norfolk Central Railway, a scheme proposed to build a line from March to Norwich, via Wisbech (connecting to the PW&SBR) and Watton (connecting to the independent Thetford and Watton Railway). https://discovery.nationalarchives.gov.uk/details/r/3e042169-424c-487b-9a20-8fe0a9b369ba