Yes I only have a blue card of my own (and also a corporate issued card in my name).
Blue participates in Membership Rewards
Express, which does not include transfers, unless the card is linked to a Green, Gold or Platinum card.
What type of Corporate card do you have and is it enrolled in Membership Rewards? Not all employers permit this. If it does, have you "linked" your Personal and Corporate card accounts? There is a fee to do this, $75 per year I believe.