"allow not only" is correct and usable in written English.
You can use it to introduce two or more ideas that are connected. For example: "Through this policy, we allow not only more flexibility, but also increased efficiency in our processes."
Better still, as this book shows, they allow not only birds but the human imagination to take flight.
For the realization of Gardner's vision would allow not only the terribly sick but the healthy to escape the horrors of death.
It will allow not only rescue workers but also volunteers, residents, schoolchildren and passers-by to apply for compensation and treatment for cancers developed in the aftermath of the attacks.
English laws of inheritance allow not only an estate but also a surname and arms to pass by eventual succession to individuals unconnected in blood with the original owner.
Scale maps allow not only the visualization of qualitative data but also georeferencing.
IL mixtures allow not only the tailoring of the working concentration interval of the cycle but also improving its performance.
Finding links with macroclimatic factors would allow not only prediction of activity but also the effects of any climate change over these communities.
These multi-level features allow not only characterization of cancer morphology, but also extraction of structural and interpretable information within the histopathological images.
These modules allow not only simple gene deletions but also more sophisticated genetic manipulations like inserting sequences for C-terminal protein tagging.
Abstract relationships allow not only the representation of dynamic interaction but also the re-specification of these systems through behavior adaptations.
The adsorption constants of a given isotherm allow, not only to evaluate the adsorbent properties of a sample, but also to determine if adsorption is favorable or not.
