The same bard who was using a Hat of Disguise on her Found Greater Steed is now thinking of picking up Mislead.
I agree with the accepted answer on the previous question, that when Find Greater Steed says:
While mounted on it, you can make any spell you cast that targets only you also target the mount
that means there is only one spell cast, it just has two targets.
Mislead says:
an illusory double of you appears where you are standing. The double lasts for the duration…
You can use your action to move your illusory double up to twice your speed and make it gesture, speak, and behave in whatever way you choose.
If the bard casts Mislead on herself while mounted, she can extend the Mislead to the Steed. As one spell with two targets, does the bard need one action from herself to run both illusory doubles, or does she run her own double with one action, and the Steed needs its action to run its own double?
Best Answer
The text "You can use your action to move your illusory double" is a spell effect upon the targeted creature(s).
If the spell normally included multiple targets, it would read that each target could use their action to move their illusory double.
Normally, you would cast the spell, and a duplicate of yourself would appear while you become invisible, that you can control with your action. In the case of find steed, you cast the spell, and you and your steed each get a duplicate while turning invisible, which you can each control with your actions.
One could argue this is an interpretation, but the alternative conclusion is that since the steed isn't "you", no one can control its duplicate, and it becomes an uncontrollable, immobile illusion. In this case, the spell Mislead is specifically hamstrung despite qualifying to work with Find Greater Steed's spell-share in the first place. This doesn't seem like design intention.