I was doing some testing yesterday and booked some FP+s for April 9th to see if the 4th would magically appear this morning. It did not. However, I went in and cancelled the 3 I made yesterday, and when I went to book new ones, I was given a 4th (Under the Sea, which I was able to switch for something more valuable). The 4th is only available 2 days in advance of the day you want it, and only if you cancel and rebook.
ETA: FWIW, the only attractions that weren't available for a family of 4 were A&E, 7DMT, the parades, and Wishes. So if you have a "high value" FP+, you take a big risk by cancelling to get the 4th. If you don't have any of these, then you're pretty safe cancelling and rebooking to get the 4th.