Just did the math for ya. This is the highest your health can get with a fully decked squad in a raid:
60118 Hp!!
How? Inaros with Vitality and Primed Vigor using a Hirudo and Sancti Tigris, Nidus max power strength, chroma max power strength built for heat, Equinox Peaceful Provocation built for Day Form and 250% PS, Trinity for constant heals and energy, Rhino Prime for crowd control, Oberon for max heals, and Another Max Power strength Nidus. All frames equipped with Growing Power and coaction drift as auras.
First to use their abilities is the equinox with her Provoke, giving +80% increase to power strength, then everybody uses a status weapon to proc their Growing Power to give +234.3125% power strength, then the Nidus casts his Parasitic Link and links up with the other Nidus to buff his parasitic link. The second nidus then links up to Chroma to multiply Chroma's power strength by 7.40265061x, who then uses his elemental ward, that has 200% more base health times the PS of ((349%+80%+234.3125%)*7.26723654785) =4910.27068% Power Strength.
48.2044884265*2 = 98.2054136 times Base Health.
96.408976853+4.4 (Vitality) + 2.2 (Primed Vigor) + .25 (Purity Effect) + .25 (Hirudo) = 105.305414 x Base Health.
Inaros Base Health is 550. 550*103.508976853 = 57917.9777
57917.9777 + 2200 (Health at Max Rank) = 60117.9777
This rounds up easily to 60118
There is a unique way to possibly make it even MORE powerful, but it requires the use of awkward and quircky game mechanics that may or may not work as intended. What you need is an Ogris with max status, radiation prioirity build and as minimal damage as possible, including a negative damage riven. Afterwards, you will need to shoot your foot with the ogris until you inflict yourself with a radiation proc, after which you can cast well of life on the inaros on your team. Well of Life ensures that the target remains suspended, all damage inflicted on him heals teammates, and also increases health by 10x!!!!
60117.9777*10 = 601179.777, which would be rounded down, so maximum amount of health on a warframe bar none is:
601180 HP!!!!!!
The End
EDIT: Completely redid this post in light of reading over something I forgot. HERE is the highest health possible in game.
EDIT 2: After doing some tests, Nidus' Link was stealth changed to not stack links to one another, thus changing the formula completely. New formula involve an Axi Run, with a Chroma, Inaros, Nidus, and Equinox. If Nidus and Chrona both get the double range and Double Strength buff, using the same formula from before, doubling nidus and chroma's PS, we get 49398.36 health as the max. 10x with trinity link, and the current TOP health is 493983.6, which would be buffed to 493984.