I could have imagined a follow up series opening with Clyde talking to camera, saying "Sarah Jane always said there comes a time when you've got to strike out on your own... so that's what I'm doing."
"Not quite on your own" says Rani's voice as she turns the camera round to show it was her filming him.
And they're off, alien-hunting on their own, with Rani working as a trainee newspaper reporter and Clyde as a freelance cartoonist who sometimes works for the paper (that comes from the vague plans that had been laid for season six so the actors could keep appearing as they chose around more adult roles elsewhere).
That would've worked. Maybe they move to another city, to explain why we don't see SJS, and they have some gizmos of their own that Mr. Smith made for them, or that maybe the Doctor left them in an unrecorded visit. But you gotta have K9 -- say SJS asked him to go with them to keep them safe.
Another possibility might've been to have another former companion take over as their mentor. The Martha Jones Adventures