Nope, only one and that is Chase, because he doesn't care, he has bodyguards.
Grayson is another story, and he is actually far more dangerous than a normal dominant alpha, he let Josh hit him. Spoiler.........................................................
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In the side stories, when Grayson get Josh for Chase ( yep, he is really helping this time), Josh gets an idea ( he still doesn't know strong he really is) how dangerous Grayson is and that he underestimated him.
And in Grayson's story it is mentioned that Josh started to train Chase in selfdefense and he started to get difficulties figthing him off.
I never said that Josh isn't a top class bodyguard. The starting comment said that Josh is stronger than the dominant alphas in this story.
You have Chase who is actually is strong, but lacks training and technique etc. So he is no problem for Josh.
Grayson is another story, because Grayson doesn't have bodyguards.
But I didn't want to go into detail about Grayson, because those are spoilers. And the only thing I mentioned is something that will happen in the extras of KMIYC. And I only did that, because Josh hitting Grayson at the hospital could give you the wrong idea about how dangerous Grayson is and that Josh underestimates him, since he didn't fight back and let Josh hit him.
How dangerous Grayson really is, you'll find out in his own story.
The secondary gender is only a problem because of pheromones. So it would depend on the client. For one if the clients doesn't want omegas in the bodyguard team or if it really can become a problem while working. Since dominant alphas in general have gammas as bodyguards, they are normaly not the clients of Mark's firm.
But no matter if Josh probably is the best bodyguard in Mark's team, it's a problems if the client doesn't want an omega bodyguard.

If ppl miss out on Joshua as their bodyguard just because of his secondary gender that'd be so stupid lmao cuz he's stronger than the dominant alphas in this story