I've just had some more ideas on how Sony can approach the spin-off/TASM films:
THE SINISTER SIX (2016):
The film has a dark tone, focusing on the Sinister Six being formed and Peter still coping with Gwen’s death and feeling guilt-ridden about Uncle Ben and Capt. Stacy.
The film introduces the symbiote, used and modified by the Goblin (with the help of Otto) as a weapon, the symbiote actually being a member of the S6 (waiting for the perfect host).
Otto Octavius and Peter are the protagonists are the film, following the two characters’ descent into darkness as Otto is driven to madness by the Goblin, becoming Doc Ock and working in the S6, and Peter coming across the symbiote and being consumed by it.
Spider-Man has a very minimal appearance in the film apart from when he defeats most of the S6 with the symbiote in a grand and epic climax, leaving only Kraven and Vulture who have managed to escape. The film ends with Peter killing the Goblin.
BLACK CAT (2017):
The solo Black Cat film sees her fighting off The Vulture who, after the S6, takes a backseat in crime and works with the mob.
Cat takes Spider-Man's place, fighting small crimes while he disappears after getting the symbiote, during and after the events of “The Sinister Six".
THE AMAZING SPIDER-MAN 3 (2018):
Spider-Man is more "Venom-like" than ever when donning the symbiote, unable to separate from it, like a drug addict.
While it was already done in SM3, Spider-Man’s greatest battle should be with himself, being very animalistic and ruthless in TASM3, more “beast” than “man” and Peter struggling to find himself again (paralleling the theme in TASM1).
Kraven is still on the loose in NYC and is out to hunt Spider-Man and kill him, now seeing him as a threat and dangerous, after seeing him kill the Goblin.
Cat believes she can save Spider-Man from the symbiote and is willing to help him but has to face Kraven and hunt him down too. Spider-Man is also aware that Kraven is onto him and prepared for Kraven, luring him into his own traps.
Cat has to face both Spider-Man and Kraven, stopping an unstable Spider-Man from also potentially killing Kraven.
Cat is eventually successful and helps Peter to escape from the symbiote, leading into the Venom solo movie where Eddie Brock will stumble across it!
The end.
I'd say that the only problem with these ideas is that THE S6 are quickly defeated in their only film by Spider-Man himself and people would confuse The S6 movie for TASM3. The symbiote storyline may also drag on for too long across two films, making the general audience bored of it and making them unlikely to see a solo Venom film.