Is it possible to update a Doc2Vec Vector?
Individual vectors can be updated, but the gensim Doc2Vec model class doesn't have much support for adding more doc-vectors to itself. 
It can, however, return individual vectors for new texts that are compatible (comparable) with the existing vectors, via the .infer_vector(words) method. You can retain these vectors in your own data structures for lookup. 
When enough new documents have arrived that you think your core model would be better, if trained on all documents, you can re-train the model with all available data, using it as the new base for .infer_vector(). (Note that vectors from the retrained model won't usually be compatible/comparable with those from the prior model: each training session bootstraps a different self-consistent coordinate space.)
I am working with a steadily growing corpus. I train my Document Vector with Doc2Vec which is implemented in Python. 
Is it possible to update a Document Vector?
I want to use the Document Vector for Document recommendations.