Is the intention of drawing closer to Allah sufficient to encompass all good intentions for deeds in general, or must multiple intentions be specified for each deed to gain greater reward, and is there a comprehensive intention for all good?

Intention is a great thing, and a believer may combine righteous intentions in an action to acquire rewards, and it is a condition for acquiring the reward.

"And indeed, for every person is what he intended" implies that whoever intends something will attain it, and whatever he did not intend, he will not attain. So, whoever goes out only for prayer will not receive the reward for visiting the sick or for praying over funerals unless he intended and purposed them. Consequently, a general intention is not sufficient; rather, for every intention that arises in the heart, the servant is rewarded for it.