For Ayyubids, you can get Atabegs to buff specific military buildings, which gives +20% HP to units produce from there. However, if you research “Biology” from the University for +20% HP to Cavalry, it does not combine properly with Atabeg Supervision, since it gives +40% HP from their natural max HP, rather than +44% HP.
For Melee Infantry with “Elite Army Tactics” (+20% Melee Infantry HP), and Siege with “Siege Works” (+20% Siege HP), they properly get a total max HP of 144% (120% x 120% = 144%).
Unfortunately, it only gives 140% HP (120% + 20% = 140%) to Cavalry.
Build: 9.1.176.0