I went through and cataloged a list of equipment required for completing Foundation 3. A lot of this is already required for F1/F2/F3. Please let me know if I missed anything or if you've come up with any clever substitutions:
FL:
rings will be sufficient
FL->iM:
need a wall or stall bars for bridge wall walks. (not really new)
sPL:
no new equipment needed (but can do on parallettes)
sPL->iM:
no new equipment needed
SL:
stall bars absolutely mandatory (not new)
SL->iM:
need some light weights (not new)
MN:
Need p-bars (not new)
Need block for elevated reverse plank (not new)
MN->iM:
Need furniture slider/slippery thing (not new)
Stall bars now mandatory (not new)
Need medium weight (not new)
Need p-bars that you can swing on. (only for the last exercise)
SLS:
need very heavy weights for lunging
SLS->iM:
need light weights and a place to do arch ups (not new)
HBP:
Need a mat/mattress/other elevated (~6-8") surface you can lay on for SE1
HBP->iM:
Need olympic bar/other very heavy bar for SE8->iM
RC:
you need a rope!
RC->iM:
a bar low enough to hang with feet support (or something you can put under a bar to give you support while hanging) for SE2->iM