Is there a way to suggest placement next to a particular app?

You can add competitor app names as keywords, or combinations of keywords that also match your competitors, which work as long as they're still seen as appropriate matches for your app (I think this goes in the black box that is 'quality'). As with all keyword matches you're not guaranteed an ad will be shown, but some of the time your app's Search Ad will appear when people are searching for your competitor's app by name for instance.

It's worth noting, things like Search Match and Broad Match will often match you against competitor apps anyhow, so there's nothing particular nefarious about doing it intentionally. However, your mileage may vary - I've seen being matched against some competitor apps perform incredibly badly for me in terms of CPA, especially when I've been matched against something I've not chosen (and probably wasn't really relevant) but it is worth experimenting with this.