"but also simultaneously" is correct and usable in written English.
You can use it when you want to indicate that there are two or more things happening at the same time. For example, "I was feeling a mix of excitement and anxiety, but also simultaneously feeling a sense of peace."
To that end, Gatti published his article not only on the New York Review blog, but also, simultaneously, in the Italian, German, and French press.
The dooup not only grabs the mess from the garden floor and stores it in a container, but also simultaneously sprays the affected area with a sanitising fluid.
In the 1950's, the worry had more to do with cold war nuclear threats; in the 1960's, there were sharp political divisions over the Vietnam War (but also, simultaneously, a flourishing shared counterculture).
This paradoxical process represents Muslim women as victims of patriarchy who need to be rescued, but also – simultaneously – symbols of radical Islam who deserve to be criminalised "for their own good".
Scott points out that, around that time, writers began to imagine a future when human beings would live not just in the here and now but also, simultaneously, on some other, more abstract plane.
"I need to experience the movie in the way everyone else will, but also, simultaneously, to reflect on that experience, to analyse my responses while at the same time allowing myself to have them.
"I'm troubled by the notion that now restaurant critics individually are expected to focus on a dining experience, but also simultaneously make casual character judgments before doling out reviews on a weekly basis," he wrote.
Without voice-over narration or talking-head interviews, the filmmaker was able not only to capture the present-tense rush and flutter of history but also, simultaneously, to interpret it.
