The tickets do not need to be bought together, but all will need to be purchased and associated/linked to each respective person's MDE accounts/profiles prior to making the selections. The accounts will need to be either all 3 managed by 1 account, or if anyone else has their own account, linked as friends and family. The time they'd all need to be linked for maximum booking period is 30 days prior for non-property stays, and done day by day; 60 days prior for on property stays, entire stay [can be] done first day..
So if it's a matter of 3 adults each buying their own ticket, or spreading out the expense over a few months as long as you meet the above, you should be able to book all 3 FP+ together.