Bio and Dia never stack with each other. A higher tier spell will always overwrite a lower tier spell (E.G. Bio II or Dia II will overwrite Bio), within the same tier the Bio spell will overwrite (Bio II would overwrite Dia II).
You can test this by casting a Dia spell on a monster, then, a few seconds later, cast a Bio spell to overwrite it. Watch the log, you will see Bio wear off but never Dia. You can also test this in PvP, but due to the altered nature of PvP in FFXI, the PvE test is better.