As of right now, there seems to be little chance of that happening. As was the case during the days leading up to the April 20 accord, the Conservatives have made it clear that they think it's time - past time, even - to resume the daily back-and-forth in the Commons - and, crucially, to do so with the full power and authority of the House of Commons. They say it's not enough simply to continue meeting through the Special Committee on the COVID-19 Pandemic, which has served as the venue for both in-person and virtual MP meet-ups for the last month.
And while the Official Opposition may have been the odd men out in April, this time around, they may get a boost from the Bloc Quebecois. The Bloc strongly opposed the initial push to return to regular sittings but are now openly musing about backing the Conservative bid for more frequent face-to-face meetings.
Speaking with reporters on Tuesday, Bloc leader Yves-Francois Blanchet pointed to his party's growing frustration over the minority Liberal government's failure to keep the promises made to secure the support of the Bloc for the April 20 deal, particularly their demand for more support for seniors as well as new measures to ensure the emergency benefits wouldn't make it more difficult for Quebec farmers to hire summer workers.
For his part, New Democrat leader Jagmeet Singh has declined to say whether he would support a full return to regular House business, although both he and his party are very open to exploring ways of expanding the current virtual meeting format to include more Commons proceedings.
In an interview with Canadian Press, New Democrat House leader Peter Julian acknowledged that "the reality is ... we can't have 338 MPs flying to Ottawa next Monday." Such a scenario "would not make sense," he noted, as it would "increase the chance that we're vectors of the virus, and we're a long way from being out of the woods."
Julian also suggested that his party might be willing to support more in-person sessions of the COVID-19 special committee, which currently holds a weekly meeting in the Chamber on Wednesdays. However, that's unlikely to satisfy Conservative Leader Andrew Scheer, who has repeatedly dismissed the idea that the special committee can serve as a "replacement for Parliament."
So, given all that, with the initial negotiations between House leaders all but certainly already underway, it's worth taking a quick look at what has changed - and what hasn't - since April 20.
For one thing, while many businesses and public services are still under lockdown, some provinces have either already begun or are beginning to ease the rigid social distancing restrictions that effectively shuttered all but essential services for the last two months - including, it's worth noting, Ontario, where the precinct itself resides, albeit not under provincial jurisdiction.
And while the House may have spent most of the last nine weeks powered down, it did reconvene for just long enough to sign off on hundreds of millions of dollars in emergency benefits and other measures aimed at mitigating the economic and social impact of the outbreak.
Those expenditures, as MPs from all sides of the House would rightly point out, should be subject to the same parliamentary due diligence as any other government initiative would be, even - or perhaps even especially - during a public health crisis.
At the same time, many businesses, services and regular day-to-day activities are still on hold in most regions - and, indeed, in most provincial and territorial legislatures.
Perhaps most crucially, though, barring dramatic sudden advancements in the field of teleportation, there's still no way to get 338 MPs from their ridings to their assigned seats in the Chamber without breaching multiple layers of social distancing protocols along the way.
As for the current practice of assembling a skeleton crew of MPs to represent their respective parties in numbers that reflect their relative House standings, that really only works on an emergency basis.
While they've been willing to bow to the request of their respective whips that they not show up for previous emergency sittings, most MPs simply aren't going to stay home while a handful of their colleagues conduct parliamentary business on their behalf.
At that point, it becomes a bona fide question of privilege - and specifically, the right that every MP has to take his or her seat, regardless of public health concerns.
Given all that, it's fair to say that the House leaders will have their work cut out for them as far as finding a way around a repeat of the standoff that led to the last deal. Stay tuned.