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The current PuTTY support for connection sharing works on the more or less ad-hoc basis that the first PuTTY or Plink to connect to a host becomes the 'upstream' (which manages the real SSH connection) and accepts connections from other PuTTY tools which automatically become 'downstreams' (talking to the upstream rather than to the real server).
A downside of this structure is that whichever PuTTY is first to contact a given host has to remain active while it's managing any connections from downstreams. This isn't a completely unfamiliar phenomenon to power users of SSH – it's exactly analogous to what happens when you end the terminal session in a PuTTY which still has X11 or port forwardings active – but it would be nicer to avoid it if possible, so that all visible PuTTYs behaved more or less similarly.
To arrange this, we'd have to have the first PuTTY spawn a separate process to act as a dedicated upstream. Then the PuTTY itself would connect to that, once it was ready, and merely be its first downstream.
This is a tricky project, perhaps as much work again as implementing connection sharing in the first place. Problems include:
ssh-userauthprotocol to the primary downstream (and pass it a special protocol message containing the cryptographic session ID for use in signatures).