We know that after Stage 2 of the LRT, there will likely be a Stage 3. Stage three will likely ignore the core and extend into Riverside (good) and Kanata (meh). No doubt the core will still be getting busier and the problem of Bank Street is going to have to be addressed.
While there are already some basic plans and ideas about a Carling streetcar, no one is talking about Bank Street or Montreal Road. Here's my modest proposal for a first stage of a Bank St. and Montreal Rd. Subway:
Yes, I know it's small to start but it's what could reasonably be called for given the population and money. The southern "anchor" is Billings Bridge because it connects to the Transitway and is an employment area and close to residential towers. The eastern "anchor" is just over the bridge on Montreal Rd. where TOD can kick off, and office towers already exist.
This 'Stage One' would be entirely underground and use the existing downtown tunnel as a starting point. Moving on to 'Stage Two', the subway would be expanded south to Hunt Club and East and south to St. Laurent.
For the eastern expansion, a good deal of it would be underground. It would run just east of St. Laurent (businesses and residential towers there) before turning south where it could emerge into an open-air trench that runs just east of St. Laurent proper. This ensures ROW without cars getting into the mix. This would require some expropriation of school and residential lands, however.
A trench would be a good idea since it ensures ROW, won't involve too many road closures, and can more easily facilitate the sharp turn off of Montreal Rd. Stops are concentrated around schools, shopping centres, and residential towers. The eastern "terminus" of the line would be the St. Laurent Centre, which also helps to create an eastern Ottawa "Rapid Transit Loop" between Rideau Centre and St. Laurent Centre, with LRT and a 'subway' being the two components.
Future expansion could continue in a secondary line that runs east along Montreal Rd. until Bathgate where it heads south. This would connect the Montfort, the edge of the NRC campus, La Cite Collegiale, and more residential areas to rapid rail transit with this subsection's terminus being Blair Station.
For the Bank Street subway south of Billings Bridge, one could largely avoid the need for tunneling. Again, this is all meant to be a modest proposal.
An old rail ROW exists just west of Bank with only one strip of houses occupying it. A tunnel would be built, slowly rising until Cecil Avenue where it becomes largely surface/at-grade rail except for when it needs to go under major roads like Walkley and Heron.
The houses east of Glenhaven Private would have to be expropriated. South of Walkley, the 'Bank St. Subway' could interline with the tracks that the O-Train uses. This prevents the need for additional expensive tunneling and has the advantage of being able to co-opt existing rail infrastructure (from Stage 2 of the Trillium Line). This also means that the 'Bank Street Subway' could also connect to the airport in such a circumstance.