Obviously, He can and does do things we can't -- ability-wise. So actually I mean "may" God do things we are not permitted to do, or should not do on moral or other grounds. What do you think?
Luke 1:26,31,35 And in the sixth month the angel Gabriel was sent from God unto a city of Galilee, named Nazareth, To a virgin espoused to a man whose name was Joseph, of the house of David; and the virgin's name was Mary. ..thou shalt conceive in thy womb, and bring forth a son, and shalt call his name JESUS. And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God.
Exodus 12:29 ...the LORD smote all the firstborn in the land of Egypt, from the firstborn of Pharaoh that sat on his throne unto the firstborn of the captive that was in the dungeon...
Exodus 13:15 And it came to pass, when Pharaoh would hardly let us go, that the LORD slew all the firstborn in the land of Egypt, both the firstborn of man, and the firstborn of beast.
II Samuel 6:7 And the anger of the LORD was kindled against Uzzah; and God smote him there for his error; and there he died by the ark of God.
Acts 12:21-23 And upon a set day Herod, arrayed in royal apparel, sat upon his throne, and made an oration unto them. And the people gave a shout, saying, It is the voice of a god, and not of a man. And immediately the angel of the Lord smote him, because he gave not God the glory: and he was eaten of worms, and gave up the ghost.
Exodus 23:28 And I will send hornets before thee, which shall drive out the Hivite, the Canaanite, and the Hittite, from before thee.
II Kings 17:25 And so it was at the beginning of their dwelling there, that they feared not the LORD: therefore the LORD sent lions among them, which slew some of them.
Genesis 38:7,10 And Er, Judah's firstborn, was wicked in the sight of the LORD; and the LORD slew him...And the thing which he did displeased the LORD: wherefore he slew him also.