对 + [noun] + 予以 + [two-syllable verb]
[noun] + (将 / 应) + 予以 + [two-syllable verb]
予以 is a formal light verb – a verb that carries almost no meaning of its own and hands the action to the verb after it. 予以支持 means the same as 支持, but it sounds like an announcement or a ruling.
Only the action follows 予以. The person or thing it's aimed at comes earlier, with 对 or as the topic of the sentence.
The action is a two-syllable verb: 支持, 帮助, 批评, 处理, 考虑, 解决, 奖励, 处罚, 批准, 采纳. A one-syllable verb doesn't fit.
给予 can take the person straight after it; 予以 can't. 加以 leans towards working on something (研究, 分析, 改进); 予以 towards actions that give or decide (支持, 奖励, 批准, 处罚). Both have their own entries, and so does the negative 不予.