Modeling an entity that surpasses our intelligence, especially one that interacts with us, is an extraordinarily challenging, if not impossible, task.
Concerning the potential for harm, consider the example of Vladimir Putin, who could theoretically cause widespread destruction using nuclear weapons. Although safeguards exist, these could be circumvented if someone with his authority were determined enough, perhaps by strategically placing loyal individuals in key positions.
Putin, with his specific level of intelligence, attained his powerful position through a mix of deliberate actions and chance, the latter being difficult to quantify. An AGI, being more intelligent, could achieve a similar level of power. This could be accomplished through more technical means than traditional political processes (those being slow and subject to chance), though it could also engage in standard political maneuvers like election participation or manipulation, by human proxies if needed.
TL;DR It could do (in terms of negative consequences) at least whatever Vladimir P. can do, and he can bring civilization to its knees.