Can chicken be partially deep fried to fully fry later?
Stephie's answer covers the main issues.  I would add that you should probably check with any government regulations about food handling.  I don't know where you are located, but many states have guidelines about how commercial cooking operations must handle "partially cooked" foods, often requiring documentation of your process, temperature and time monitoring records, labeling of all partially cooked containers (and separation from other raw or cooked food), etc.  In the U.S., these are often closely related to the FDA Food Code.  (Partial cooking regulations are generally a little more complex than any "2-hour" or "4-hour" rule which is often brought up here.)

Particularly if you plan to try Stephie's 3rd method of partial cooking followed by cooling to refrigerate or freeze, there are generally very specific practices about the amount of time spent during partial cooking and the amount of time spent cooling (sometimes in specific temperature ranges).  Usually this method is best for bulk batches prepared in advance, so you have time and attention to monitor the process.  That's why most fast-food restaurants that use this method tend to do this as a large-scale industrial process in advance, then ship out the partially cooked frozen or refrigerated food to be simply heated and served.

And if you are going to try to implement Stephie's 2nd method (holding for short times without temperature control), you'll want to have logbooks to keep track of holding time and label every container of partially cooked food.  You'll also need to be absolutely certain to keep various batches separate to avoid cross-contamination between partially cooked food, particularly if some of the food may not have reached 140F before holding.

In general, the safest and easiest thing to do is generally to bring food to at least 135F and hold it there.  (I should note that the 2013 revisions of the Food Code say 135F minimum for holding, instead of 140F; this change has not yet been implement in most FDA consumer guidelines, but it's now the standard for commercial cooking.)  Trying anything else requires a lot more attention to detail to prevent potentially dangerous bacterial growth.  That's the reason behind the complex Food Code regulations covering partially cooked foods; there's a much greater likelihood of making people sick if you're not careful.