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Here is what the ISS would look like without the Russian Segment attached - in it's place, a Dragon could be docked to provide reboost capability and attitude control.
With Cygnus near to Dragon on the aft end of the station, and two Dragons docked to the forward end, this would give very good attitude control capability, and provide multiple reboost options.
An International Docking Adapter (IDA) would need to be attached to Pressurised Mating Adapter-1 (PMA-1), which is where the Russian Segment is currently docked to.
Adding the IDA shouldn't be a problem, as PMA-1 uses the same APAS docking mechanism as PMA-2/3 on the forward end of the station, which already have IDAs attached.
Cygnus could also potentially be modified to dock rather than berth, in order to provide more reboost options - although it is capable of performing reboosts from its berthing location underneath Node 1.
Dragon could also potentially be modified to carry an additional engine & fuel in the Trunk. One thing Russia ought to have learned over the last few years is not to underestimate the innovation of the US commercial space sector. ISS could survive without them. @Rogozin @elonmusk
This plan would also ensure that there would always be one vehicle present on either end of the station even during vehicle swap-over periods, which would be helpful for attitude control.
Since Dragon's main Draco engines are located on the forward end of the capsule, they face the wrong way when Dragon is docked to ISS. For this reason, a better option would be to develop a stand-alone engine/fuel package that could fit inside the Trunk.
This could actually be beneficial, as it means that no modifications/re-certifications would need to be made to the Dragon capsule itself. It also means that Dragon would not need to use it's internal fuel for reboosts.
NASA should call Rogozin's bluff on his rhetoric and immediately instigate a plan to modify commercial vehicles to provide attitude control & reboost capability. Even if it's never needed it will be good to have as a back-up option.
They should also begin a quick-look study into what would be required to undock the Russian Segment. In theory it is possible, you'd just need to close the hatch and send the undock command, and a pair of these.
In this scenario, it is the Russian Segment that would be screwed, as it wouldn't be able to generate enough power to support itself without the US solar arrays. So Rogozin ought to be careful with his statements!
Upon further reflection of the above, Dragon is likely not the best option to provide propulsive support, due to the orientation of it's main engines, and the fact that it needs to always retain enough propellant to serve as a crew lifeboat.
The best option would probably be to develop a Cygnus with a docking system (NDS), rather than a berthing system (CBM). This way Cygnus could provide reboosts from either the forward or aft PMA, which would give thrust along the station's main axis.
But, there is an issue with this too - Cygnus currently launches on a Ukrainian-sourced rocket, with Russian engines! For this reason Cygnus should be certified to launch on Falcon 9 ASAP.
This plan btw would also provide ISS with a much-needed third docking port, which would be highly useful!
A further addition to this thread: I'm not proposing that NASA immediately *implement* this plan, I'm proposing that they immediately *develop* this plan. The purpose would be to send a message to Russia that NASA has viable options to run ISS without them.
This in turn would make Russia realise that they too stand to lose from their dangerous rhetoric, and bring them back to the table as a partner rather than a bully. However, NASA should be fully prepared to implement the plan if necessary.
Another important point: SpaceX should accelerate their efforts to make Dragon capable of seating 7 crewmembers. This would mean that all ISS crew could be rotated on a single Dragon, which would free up another docking port on ISS for reboost vehicles. @elonmusk
I should also add that I would be sad to see the ISS partnership end this way after nearly 25 years, but unfortunately Russia's actions have made it untenable, and "partners" that use their capabilities as tools of threats and intimidation are no longer true partners.
The West collectively needs to send a strong signal to Russia that we have the impetus & ability to support ourselves, and not be dependant on them, nor cowed by their threats. The ISS could be one important way of sending that message, in a way that would have a tangible impact.
Yet another point - the "life limiter" on the ISS is most likely going to be the Russian modules (one is already leaking). But without the Russian modules, ISS could probably fly on past 2030, which means it could be turned over to a commercial operator.
When the time does come to de-orbit ISS, the best option would be to ask the Europeans to build a version of their huge Automated Transfer Vehicle with a NASA Docking System, rather than a Russian docking system. This vehicle is already designed and flight-proven.
TL;DR: The ISS is actually one of the only non-military options the West has to inflict some serious near-term consequences on Russia. Undocking them from ISS would effectively terminate their crewed spaceflight program. That would send a strong message.
Recap - here's the three things that @elonmusk could immediately do to support ISS:

. Begin development of a propulsion package for Dragon's Trunk

. Begin an effort to certify Cygnus to launch on Falcon 9

. Accelerate efforts to increase Dragon's crew capacity to 7
(Such a propulsion package could also have benefits for higher-orbit Dragon missions, such as @rookisaacman's @PolarisProgram).
As we've discussed in this thread, NASA is arguably in a much stronger position to go it alone on ISS than Russia. NASA has a very capable commercial space ecosystem that could provide multiple propulsion options.
Russia's cash-strapped space agency by contrast would have very limited options to provide power for their ageing modules. They of course know this, their rhetoric is a bluff. Don't fall for it. @Rogozin
Another valid point to consider however: Once Russia no longer have any "skin in the game" on ISS, Putin could effectively deny the use of Low Earth Orbit to the rest of the world by conducting multiple ASAT tests. And he's probably crazy enough to do it.

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