It is sad we can never establish if Shakespeare coined any new words. One seems to need an expression, but even in that case ‘mind’s eye’ might have been lifted from the vernacular or elsewhere unlike “The sea, the snotgreen sea, the scrotumtightening sea.”
It seems likely Shakespeare was a pal of Marlowe and he certainly acknowledged his influence: Marlowe’s line in Hero and Leander was used in As You Like It (’Dead Shepherd, now I find thy saw of might, “Who ever loved that loved not at first sight?“‘).
Thirty years ago I remember reading a book by someone who reckoned Marlowe wrote Shakespeare’s works and he had loads of examples of similarities in their versifying. All I could find online was:
Holla, ye pampered Jades of Asia.
What, can ye draw but twenty miles a day....
Shakespeare’s Henry IV (Part II):
And hollow pampered jades of Asia,
Which cannot go but thirty miles a day.
Marlowe’s Dr. Faustus (conjuring Helen of Troy):
Was this the face that launched a thousand ships?
Shakespeare’s Troilus and Cressida (referring to Helen of Troy):
... She is a pearl,
Whose price hath launched above a thousand ships.
I count religion but a childish toy, And hold there is no sin but ignorance.
(The Jew of Malta)
I say there is no darkness but ignorance.
Weep not for Mortimer
That scorns the world, and, as a traveller
Goes to discover countries yet unknown.
The undiscovered country from whose bourn
No traveller returns.
A bit tenuous. I am not suggesting M was S but in those days plagiarism and embellishment weren’t sins, as with Shakespeare’s use of other sources like Hollinshead, etc.
‘Nice line, Kit! I’ll use that now you’re dead.’ Nor was Shakespeare writing for posterity, just ackers, though his fellow poets might have appreciated any allusions if any were detected.