OK, the Tleilaxu can engineer life in the form of things like ghola and “twisted” mentats, and I remember something being written about their creation of custom labor forces for certain clients. But what about blatantly posthuman creations? In a universe where warfare has largely devolved (evolved?) into a largely hand to hand affair, wouldn’t masses of disposable yet suicidally ferocious cannon fodder find an eager market? What about heavily enhanced “super soldiers” for when skill, strength, and durability is a must - but subtlety isn’t?
Has there been anything like this in the books?
Speaking only about the Frank Herbert books, there is nothing about Tleilaxu cannon fodder. I think there are a few reasons for this: blatantly post-human creations are anathema to the members of the Imperium. Where some things that skirt various prohibitions might be acceptable (certain machines, for instance) anything large scale would draw negative attention from the Landsraad. Keep in mind that espionage and subterfuge are coins of the realm; keeping a mass of “suicidally ferocious cannon fodder” a secret would be nearly impossible, never mind prohibitively expensive. Only a Major House would have the wherewithal to afford it. And should the Emperor sniffs out that a House is creating such an army, it would be a sure bet that a legion of Sardukar would come calling.
(Disclaimer - I am an Orthodox Herbertarian, so I cannot speak to what Brian Herbert/Kevin J Anderson might have written.)
Nearest thing I can think of to their making a Super Soldier is Duncan from God Emperor.
He was already one of the closest things in the core books and it was mentioned in the DE that at least one of the Gholas was modified to be a superior specimen.
The Guild & Bene Gesserit also factor in here. They have a vested interest in keeping the balance of power in the Imperium stable. Having super soldiers around might not only mess up the power balance it might seriously mess up the BG breeding programme.
They may not have much raw power but those 2 Factions can easily sway Houses with subtle words and tweaks to shipping rates.
“Shipping troops from the Thalim system? That will be 15 million Solari, please. Cash up front. No, we aren’t offering insurance this time…”
Another thing that comes up in the later (Frank) books is that the Tleilaxu are devoutly religious themselves.
They may well have strictures themselves about twisting creatures in certain ways. Creating clearly superior forms of Humans or Animals may be seen as blasphemous to them. Call it stepping on God’s toes.
In Heretics and Chapterhouse, we’ve got the Futars, who are some sort of human-animal hybrid created specifically to kill other humans, and presumably it was the Scattered Tleilax who were responsible for them.
And we also see in those books that the Tleilax are perfectly capable of creating “products” that are more capable than they intended, and which escape their control.
So, while I agree with the posts above that they likely wouldn’t create a whole army of them, and certainly wouldn’t sell such an army to anyone else, on a one-off or small batch basis I can definitely see the Tleilax creating nigh-unstoppable super-soldiers.