How should I appear to her as romantic interest if I don't spend as much time as her male friends do?

I don't spend as much time with her as her male friends do since they have their own lives, and while most of them do have friendship in mind, some men she apparently views as friends had told me that they wouldn't say no to a relationship with her (although she knows about these relationships already).

What activities should I suggest to her in order to surpass the potentially competitive men while not letting this seem like she was a price to win?

How should I appear to her as romantic interest if I don't spend as much time as her male friends do?
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