In relation to Shankara, She manifests many forms such as Meenakshi, Lalita Tripursundari, the ten mahavidyas, etc. and sports with Him in various ways for the benefit of the followers of tantra.
When desiring to establish Her own glory, She assumes central importance in celestial wars and is declared as the amalgamation, or rather, the source of Shaktis of all other devas viz. Brahmani, Kaumari, Vaishnavi, Aindri, Varahi, etc. This deity of Durga although seemingly beyond the figure of Uma or Parvati, the spouse of Shankara, is indifferent from Her.
As an act of leela, and substantiating Their individual glories amongst Their countless devotees - those innumerable spiritual associates of glowing bodies in Vaikuntha, Kailasa, etc. They worship each other in various ways. In Rameshvaram, Sri Ram became Sri Shiva and Shiva became Ram. Puranas speak of a particular Ramavatar, where Lalita-devi/ Durga descended as the green-hued Ramachandra and Her spouse, Shankara became Seeta. Indeed, a saint, who has received the title Jagadgurrottam (the best of all Jagadgurus viz Shankara, Ramanuja, etc.), reveals that Parvati became Sri Krishna once and Shivji became Radha. Parashuram serves Devi in various ways and so does Hayagreev. Both are incarnations of Vishnu.
Shiva, in the form of Hanuman, serves Ramachandra and enters the Raas-leela in a gopi form whereas Gadadhar Vishnu incarnates Himself as a certain Paramhans and worships Bhavatarini Kaali in Eastern-bharat varsh.
Of course, God has infinite Forms but They can only ever be classified as Shakti-tattva, Shiva-tattva and Vishnu tattva. What about Ganesha, Kartikeya, Saraswati, Brahma-deva, Surya-deva, Hanuman, you may ask? Even these forms are associated with the said three divinities.
Ganesha is said to be a form of Sri Krishna, Kartikeya, the combined manifestation of Shiva and Vishnu, Surya, an expansion of Sri Vishnu, etc.
The conclusion, my dear readers, is that you should equally respect and adore all these divine forms of God: Sri Krishna, Sri Ram, Sri Durga, Sri Shiva and Sri Vishnu, and constantly dwell upon their wonderful indifference and charming interactions – a mere fraction of which has been put together here.
EDIT: I am a big fool, and this information has already been freely broadcast by the great Acharyas of the Vaishnava tradition.