This past fall's "Invasion!" crossover between "Supergirl," "The Flash," "Arrow" and "DC's Legends of Tomorrow" was rather ambitious -- but maybe not quite as ambitious as some may have liked. While the story encompassed characters from all four of The CW's DC Comics-based superhero shows, it only truly encompassed three of them -- that week's episode of "Supergirl" was mostly business as usual, other than a short lead-in scene that also ran in "The Flash."

For the next full-scale Arrowverse crossover -- which is tradition holds, will likely be in the fall -- the creative forces behind the show are hoping to fully involve all four series, according to Andrew Kreisberg, an executive producer on each one of the shows.

"Next year, we’re hoping to do a true four-way crossover," Kreisberg told reporters, including CBR, during a press event Friday at The CW's Burbank headquarters. "Right now, the great thing about our dear friends at The CW and [The CW President] Mark Pedowitz picking the shows up as early as they did has allowed us to start building the schedules for next season."

With the early renewals, Kreisberg explained, the shows can take advantage of pre-planned off-days in production to accommodate the cast members who are appearing on multiple shows in a short time, something that was particularly difficult last year with "Supergirl," since series lead Melissa Benoist appeared in both a normal episode of her show, and then as a guest on "The Flash," "Arrow" and "Legends."

"'Supergirl' was the show we needed to shut down the most, and it was the one we didn’t have any opportunity to," Kreisberg said. "So now that we’ve gotten the early pick up and we’ve started designing the seasons, we're building in those dark days -- and actually more dark days on 'Supergirl' than the other shows -- to make it a little easier."

The first full-speed Arrowverse crossover happened fall 2014, between "The Flash" and "Arrow" (the only two Arrowverse shows at the time), though it functioned more like two loosely related episodes of both shows, which guest-starred each other's cast. The second took place in 2015 -- when "Supergirl" was still on CBS, and not yet connected to the Arrowverse -- and served as a prelude to "Legends of Tomorrow."

Last year's crossover, inspired by the "Invasion!" event from 1980s DC Comics, ended with Supergirl receiving an interdimensional transportation device to get her between her Earth and the Earth where "Arrow," "The Flash" and "Legends" all take place. The next crossover between "Supergirl" and the Arrowverse will be March 21's "Duet," an upcoming musical episode of "The Flash" featuring members of both shows' casts, with a lead-in on the previous day's "Supergirl." And it's not just CW superhero shows that will be represented -- Rachel Bloom, star and co-creator of The CW's "Crazy Ex-Girlfriend," co-wrote a musical number for the episode.