The "with" suggests that she will be involved.
Without the "with" you might be told to go do the crimes, while she sit in her armchair watching TV.
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I'm not sure what you want. Examples of phrasal verbs ending in "at" and "on".
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I need a wall to throw this at. (throw something at something- phrasal verb)
Get me a plate to put this pizza on. (put something on something - phrasal verb)
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English is something that you can be good at (good at)
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He's on the horse again. Get him off.
Get me a box to put this in. (put something in something)
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Where are you at? :)
Hope it helps.