I think all Christians agree that:
1. God cannot do evil - His nature is to be Good - this is a Good God
2. God cannot do anything illogical, self-contradicting
So all Christians have a concept of God that is somewhat bounded, somewhat limited - and this applies even to the God of Classical Theology who is conceived as almighty, omnipotent, all-knowing and present in all places.
What is relatively neglected - and in a way which may be harmful - is that God is also limited by free will; He cannot violate human free will - humans are autonomous agents of will - centres of choice.
God awaits the result of Man's free will - God can plan up to that point, and from that point; and mobilizes incomprehensible and effectively-infinite power up to and beyond that point - but Man's free will stands apart from this.
The whole plan of salvation, the sacred history of Scripture, is predicated on this - on the fact that Men must choose, that their choice is real; and only because Men can choose, and because their choices are real is it just for the consequences of these choices to be treated as Good or evil (virtuous or sinful).
Thus we should add a third limit on what God can do - God cannot violate Man's free will.
These constraints can be expressed as what God must do, as well as what He cannot do.
1. God must be Good
2. God must be rational
3. God must work with Man's free will, must take account of the consequences of Man's agency.
This fact of Man's agency and free will is treated as theologically controversial, and indeed it may be theologically difficult to explain - but it needs to be accepted upfront and explicitly that what we are doing in life is the real thing - that our reflections and decisions are truly and ultimately our own - that we are responsible (awesomely responsible) for our lives.