"but also always" is correct and usable in written English.
You can use it to emphasize an idea or point you are making. For example: I strive to be kind and generous, but also always honest.
He always prefers pleasure to Puritanism, but also always prefers wisdom to pleasure.
As Fallingwater demonstrates, Wright's genius was always specific, but also always lively, always daring.
Such ties were personal but also always in the service of experimental investigation and scientific theory.
Bleak yes, often, but also always pointed and arresting, and sometimes – in Beckett's inimitably self-aware way – extremely funny ("I'd give up if I hadn't").
And indeed, Baker's erotica is witty and playful, but also always thoughtful.
I am at peace, but also always moving, and then I turn the corner.
But I also always felt the pressure to get things right, and be a high achiever.
Not only is Rick handsome, but he also always says just the right thing.
But I also always expected to win, and the two were strangely complementary in my mind".
But they also always used Chinese workers, often distant relatives and friends of relatives.
