to broaden the options, to widen the scope, to cast a wider net
Antes de escolher a faculdade, vale a pena abrir o leque e visitar mais de uma cidade.
Before choosing a university, it's worth broadening your options and visiting more than one city.
Aulete and Priberam define leque as a folding hand fan and, figuratively, as a range of things, as in um leque de possibilidades. Neither entry lists abrir o leque or explains how it formed, so the fan spreading open is only the literal image.
Source: Aulete — leque; Priberam — leque.
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