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Hi there!

I am trying to write a leter of intent and I came across this problem:

"I have already established a fruitful collaboration with Prof. X, that I would like to bring further by studying at your university."

2 questions:

1. I am sure "bring further" makes no sense in the context. What I mean to say is "develop even more", go further with our collaboration", but I need a phrase that seems on the tip of my tongue.. Could you help me with this phrase?

2. Is "by" ok in the context? (showing the means by which I would like to develop my collaboration with the Prof.)

Thank you very much, I hope my questions were clear enough...
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1) Why not simply "develop further"?

2) "By" is fine.
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These are not phrasal verbs, but might suffice:

foster, cultivate, strengthen
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Comments  
1. It sounds fine, I was just wondering if there isn't any phrasal verb with the same meaning though?

2. Thanks!
 AlpheccaStars's reply was promoted to an answer.
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