I think your question is very good. It's a question I asked myself often and I still try to answer. I would love to see more writers who have the poetic style of Shakespeare as their influence rather than his plots, his characters and themes.
Unfortunately it is very difficult to find other authors who try to imitate his style (and, in doing so, create their own art). I think this is due in the first place to the fact that the most decisive item in Shakespeare's art is an extraordinary abundance of metaphors, and such a metaphorical exuberance is something few poets are capable of doing. As Aristotle said:
>The greatest thing by far is to be a master of metaphor; it is the one thing that cannot be learnt from others; and it is also a sign of genius, since a good metaphor implies an intuitive perception of the similarity in the dissimilar.
An author who perceived this aspect of Shakespeare's work - a notoriously intelligent and capable author, an author whose artistic concern was primarily a concern with verbal style - was Nabokov. About Shakespeare he said the following:
>The verbal poetical texture of Shakespeare is the greatest the world has known, and is immensely superior to the structure of his plays as plays. With Shakespeare it is the metaphor that Is the thing, not the play.
It is not by chance that he has been able to read Shakespeare's work so well. He himself was highly influenced by him, and part of his art was very similar to that of Shakespeare.
So I suggest you Nabokov in the first place. He has a language that is crowded with metaphors, like Shakespeare (but not in the same degree). You could even look for a play he wrote, "The Tragedy of Mister Morn". Read the preface:
amazon.com/Tragedy-Mister-Morn-Vintage-International/dp/0307950662
in it you will find a study of Nabokov's style and Shakespeare's influence on him.
Other authors I can name are:
>Aeschylus (a lover of metaphorical language in drama many many years before Shakespeare)
>Melville (read the essay of F.O. Matthiessen, in American Renaissance, about Melville and Shakespeare)
>Pablo Neruda (a lover of metaphors, but somewhat clumsy and not also a creator of characters and stories)
>Bruno Schulz (short-story writer, a lover of metaphors and similes)
Of course, none of those authors do the same with language as Shakespeare. I will try to think on more examples. If I remember others I will name it.