I often see projects at my company that are full of part-time developers, meaning they work some % on different projects. 

Additionally, management seems to be on the Agile hype train. I feel that the agile methodology does not work well with part-time developers. How do you best manage the project with things like tasking when at any time some members may run hot on their other project(s)?

Even things like making a Gantt Chart get confused in the fact that you allocate a time for a task, i.e., 4 days, but I do not know of a way to consider that those 4 man-days may be 8 calendar days.