Yup. You can only carry one at a time. I picked up my four star when I already had one and was somewhat pissed but made a wish and then went on to dragon ball grinding again and got the four star ball within about 2 minutes of making my last wish so it was all good in the end. Also, if we do not pick up these dragon balls on those dates do they disappear or stay until you pick them up? I have not logged in in a couple of days due to being sick and getting massive headaches while trying to play this game lol