The phrase "perhaps might" is correct and usable in written English.
You can use it when expressing the possibility of something happening. For example, "Perhaps they might come to the party later."
But an e-mail, perhaps, might feel less intrusive.
How few, perhaps, might have Podolski in their scrap books?
The person doesn't look tipsy, but perhaps might be not be feeling well.
The more nuanced question, perhaps, might be: how did it go so wrong, again?
To say they are different, nonconformist perhaps, might be a virtue.
Does it benefit us in any way — or, perhaps, might it harm us?
More seemly, perhaps, might have been a little sympathy for the addict.
But this, perhaps, might mean Janine being exposed to criticism herself.
It relied more on the judgment of the dictionary user, who perhaps might have welcomed a little more guidance.
This, perhaps, might have worked out well — evacuation did work out reasonably well for thousands of others.
This, perhaps, might have worked out well evacuation did work out reasonably well for thousands of others.
