I'm far from an expert but I'll try to give you a reply
/boot 20M -- I think most distributions suggest a /boot of more than 20 Megs, and You could just install to the MBR if you want to save a partition.
/ 500M -- You will need a / partition for each distro, otherwise they will basically be one big distro.
/usr 5G -- this will be fine if you wanna all your programs and such installed for all three distros and assuming all three have the same libraries installed and such, I'm assuming the point of three distros is for three seperate OS's not 3 ways of accessing the same one...
/usr/local 15G -- same as above, unless you have a good reason for sharing/separating stuff in /usr/local I'd just leave it as part of the / partition for each distro.
/home 15G -- this is a good one to share, 15 Gigs is only needed if you will have a lot of data or programs you download w/ non-root access to be held here. Or if you install from source (.tar.gz) files and unpack them in /home.
swap 1G -- do a "free -m" in your mandrake distro right now when you have a few programs running to see if you actually need a gig of swap...the important numbers are those w/out the cache and buffers. You may not even be using your swap partition right now. But it will share fine if you want.
/tmp 500M -- not sure at all why you would make this it's own partition...again I'd say this is better left as part of the / partition for each distro.
/var 1G -- don't know bout this...sorry
Over all I'd suggest this scheme for you. if you have a 40 gig harddrive which I think you do.
/ for first distro -- 11 G
/ for second distro -- 11 G
/ for third distro -- 11 G
/home -- 6 G
swap -- 500 M
/etc -- 500M (check your mandrake install and times it by 3 and add a little to be safe)
having a /etc partition will allow you to keep a lot of your customizations alive even if you switch distros again, plus it will make all distros configured more or less the same. It is not needed though. Hopefully I am not way off here, if I am someone please help his poor soul :P