so, predicament - I take Chapter master on Bike, with Artificer Armour, Storm shield attached to Librarian with command squad and apothecary.

Apothecary gives FnP - 5+
Iron Hanhands Chapter Tactics - 4+
Gorgons Chain - 3+
Clan Raukaan Warlord Trait that gives additional +1 to FnP = 2+ feel no pain roll.

or

Endurance - FnP 4+
Iron Hanhands Chapter Tactics - FnP 3+
Gorgons Chain - FnP 2+
Clan Raukaan Warlord Trait that gives additional +1 to FnP = 1+ feel no pain roll

Don't overlook FNP not being classed as a save as BRB states "When a model with this special rule suffers an unsaved Wound, it can make a special Feel No Pain roll to avoid being wounded (THIS IS NOT A SAVING THROW and so can be used against attacks that state that ‘no saves of any kind are allowed’, for example those inflicted by Perils of the Warp)."

and under maximum save in BRB

"Some models gain additional benefits from rules that may increase any of their saves by +1 or +2 or even more. However, no save (Armour, cover or invulnerable) can ever be improved beyond 2+. Regardless of what is giving the model its save, a roll of 1 always fail."

now FNP is not a save and so doesn't fall under the limitations of 'Regardless of what is giving the model its save, a roll of 1 always fail.' stated under Maximum save.

bare in mind this is not something I would run, but looking for reasons why you couldn't take this.