After Crisis, I can see the following crossovers:
Superman/ Supergirl
Superman/ Flash
Superman/ Black Lightning
Supergirl/ Batwoman
Flash/ Black Lightning
Supergirl/ Star Girl
Batwoman/ Black Lightning
Legends/ Green Arrow and Canaries
If speculation is to be believed, and all the shows take place on the same Earth once Crisis is done and dusted, then all shows will have the potential to crossover with each other. The exceptions are probably going to be Star Girl and the Canaries show because they're time displaced; although that shouldn't be too big an obstacle when you throw Legends and Flash into the mix, cause they can time travel.
I do think there's more potential with Supergirl and Batwoman though, and Black Lightning and Flash (and obviously Superman and Supergirl). I'm not quite seeing Superman and Black Lightning however; the two characters just seem worlds apart. No doubt they'll team up Barry and Kara at some future points too, cause they've got a good friendship.
I honestly don't see Batwoman renewed for a second season. Especially since the ratings for the show are the lowest in the cw. I'll be very surprised.
I expect Batwoman will get a second season, most CW shows at least get that, but I'm not seeing, nor hoping for a third. The same goes with this Canaries spinoff.
As negative as it is for me to say, I hope both Batwoman and the Canaries show fail to draw in enough watchers to remain on air, and then another, more worthy show will come in to take their place. Batwoman just doesn't
do anything for me - maybe I had my fill of Gotham when watching Gotham. The Canaries spinoff (in my mind) is just destroying the Green Arrow Legacy, and we simply don't need it.
The CW doesn't really need any more than six DC shows to be a success. There's such a thing as overkill. Arrow, Flash, Supergirl, Legends, Black Lightening, Batwoman. That's what we've got so far. Arrow is obviously wrapping up soon, with Legends, Black Lightning and Batwoman (I think) being less than favourable shows (simply lower ratings). Flash and Supergirl I think are still strong.
If Batwoman falls, simply have that replaced by the Superman show. Ditch the Canaries, for Stargirl, and maybe replace Black Lightning with another show like the Outsiders (featuring Black Lightning). Legends is an oddball in it's own right, but that can be succeeded by the Green Lantern Corps show for cosmic appeal.