To further strengthen my graduate school application, I studied Spanish in Argentina for a semester.
The wording seems redundant and awkward to me, but it's common and I'd like some SE users' input.
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You could strengthen your application by doing X, but the next step would be to further strengthen it by doing Y.
Most of the time, strengthen would be more than adequate to use in these examples, but if you're providing a list of things to help your application, then the second, third, and fourth things you did may be further actions.