JP is already sci-fi, I would say
Obviously. It's astonishing that anyone would think it wasn't. Godzilla and King Kong are fantasy. There's no science that could justify the existence of creatures that size.
Jurassic Park is science fiction by the textbook definition, in that it's fiction driven by conjectural scientific innovation or discovery. More than that, it's specifically
about the science, about scientists debating the ethics and consequences of scientific research as well as using their scientific knowledge to survive a crisis created by the irresponsible use of science. It doesn't get much more
science fictional than that.
Mission: Impossible has always been borderline science fiction, often relying on technologies that don't exist in real life, like perfect masks and voice duplication. The original series often did plots involving computers more advanced than what was possible at the time, and the 1988 revival series often relied on fancifully advanced holograms to fool the marks. Although those are rarely more than surface trappings. At heart, what makes something science fiction is that the conjectural science or discovery is what makes the story happen, that the story would not occur without it. Technically you could say that about some installments where the mission is to retrieve or prevent the use of some dangerous scientific breakthrough, but such things are usually just MacGuffins, excuses for the spy caper that could be swapped out for just about anything, and thus still little more than surface trappings. (M:i:III lampshaded this with the Rabbit's Foot, pointedly avoiding telling us anything at all about what it actually was.)
To the basic question of the thread, I think it's generally unwise to change the tone of a series too drastically. If you've established a certain style or level of credibility, it's best to stick with that, or you risk undermining the consistency of the universe or alienating the audience. It can be done, to an extent;
Arrow managed to ease in more fanciful elements gradually after its initial, grounded season. But even so, even now that it shares a universe with shows involving time travel and magic and parallel universes, it still feels incongruous when
Arrow itself does storylines driven by evil magicians or a multiverse-threatening crisis. It's better for a given show to stick to its own lane, its own specialty and style, even when it shares a reality with more fanciful shows.
But it can hurt an SF show if it starts out with relatively plausible science but then gives way to more fanciful ideas. If a fictional universe starts out fanciful, that's fine, but if it establishes itself as grounded, plausible science fiction, then suddenly injecting fantasy nonsense undermines its believability. Too many shows have suffered when showrunners trying for credibility have been replaced by showrunners who didn't care or were too ignorant to understand the difference between SF and fantasy, so that the plausible worldbuilding gave way to sheer inanity (e.g.
SeaQuest DSV or
Gene Roddenberry's Andromeda -- or
M.A.N.T.I.S., though its first half-season about fighting urban crime and corruption was almost as bad as the more
X-Filesy second half).
As for non-SF shows being retooled as SF, I'm sure there must be examples other than
Arrow, but nothing comes to mind. Outside of TV, though, the
Dick Tracy comic strip qualifies. It was traditionally a hardboiled crime comic, although Tracy often used sci-fi gadgets and techniques in his crimefighting, like his iconic 2-way wrist radio/TV. But in the '60s, the strip swerved into outright sci-fi with spaceflight and a civilization of Moon Men becoming recurring characters. Tracy's son even married a woman from the Moon, who was a regular character for years, then eventually quietly dropped when the strip became more grounded again.
