The phrase 'altogether impossible' is correct and usable in written English.
It is typically used to express that something is entirely impossible, with no possibility of occurring. For example, "It is altogether impossible for us to get the project finished in the next 24 hours."
This did not seem altogether impossible, for a while.
Looking at the shelves now it didn't seem altogether impossible.
Unfortunately for him he had overlooked some pretty fundamental chemistry and come up with an altogether impossible structure.
It is also given under conditions which at present appear to be making the higher forms of music altogether impossible to maintain.
That a Rebel drummer boy might discover an affinity with an escaped slave instead of shooting him would not have been altogether impossible even during the American Civil War.
It is not altogether impossible that the Conservatives will argue so well against the euro in the remainder of the campaign that, even if they lose, public opinion on this issue can never be reversed.
When Tovey edited the sonata, he dismissed the first-movement marking altogether as impossible.
Eliminating that risk altogether is impossible, but if regulators act now while the rules are still malleable, they can make such crises less likely and reduce their harmful effects.
The transcendental slow movement, the hymn of thanksgiving, which is both the architectural and emotional heart of Op 132, suddenly takes off into another dimension altogether, one impossible to define in terms of the norms of the classical or early romantic eras.
Or it could make it impossible altogether.
In poor countries, the refrigerated transports and even electricity at medical clinics is often missing altogether, making vaccination impossible.
