How are Supererogative acts even possible in Catholicism? God, through each person of the Holy Trinity, the Prophets, the Saints, and his people set out what to do in order to enter the kingdom of heaven through the commandments, through the beatitudes, though lives worthy of imitation (in the case of Jesus and the Saints) and building the kingdom of God (e.g. as specified in Matthew 25).  Obviously the list is not exhaustive, but suffice to say, there are clear duties set, and reasons as to why these duties help build the kingdom of God.

Those who thoroughly practice the Catholic faith strive to go beyond the minimum duties through the forces of Grace. Striving for the minimum understandably does not help much for a relationship with God, and thus it makes sense to go beyond "what the instructor specifies" so to speak. 

But if God, who is the perfect instructor, lays out what to do for us to become perfect and thus be able to enter the kingdom of heaven, why must we go beyond what a perfect omnipotent being guides us to do?  I am struggling to understand why Supererogation is a thing.  Aren't those who follow God's law, in both spirit and letter already desiring to become perfect? How can we go beyond what God commands?  How can one go beyond desiring to become perfect?  

I feel I am missing something here, but I hope readers understand my logical conundrum here.
I've misplaced my copy of David Heyd's Supererogation or else I'd quote it directly, but that's among the seminal texts you'll want to read for a Catholic view on this topic.  In lieu of that, Standford's Internet Encyclopedia of Philosophy has great article on the topic.

I think your key misunderstanding comes in here:


  why must we go beyond what a perfect omnipotent being guides us to do? 


What I think you have in mind is that there are a set of things God requires us, but there is also a level of goodness that we can opt for beyond that.  For example, God's law required Israel to leave the corners of its fields unharvested for the poor and indigent, but farmers could also have chosen to leave more of their land the indigent if they so chose.

However, what makes an act truly supererogatory in the sense used in Catholicism is that it goes above and beyond what someone could reasonably be compelled to do.  We could reasonably compel a certain farmer to give more if there were enough people in need in the countryside, but one could not compel a farmer to give his entire harvest to the poor--that could devastate the farmer's livelihood.  Nevertheless, if a farmer chose to give his entire harvest to the poor, we would understand that he has done a very great good, a supererogatory good.  Supererogation arises out of the awkward place we're put in by acknowledging that the farmer's actions are good but yet no one could reasonably say that one is morally obligated to follow such an action.  What is good is bad not to do, and what is bad is good not to do, but what is supererogatory is good to do and not bad not to do.

For Catholics, this makes for a nimbler approach to ethics.  Because salvation in Catholicism is contingent on our continued friendship with God within the salvific cycle of sin, confession, penance, and Eucharist, it would be a pretty big problem for Catholics to be compelled to go to the absolute greatest level of goodness on all actions, because such friendship would seem impossible.  For Protestants, who typically deny the existence of supererogatory acts, the inability to carry out such profound acts of goodness is precisely what's of value, because it rids us of any illusion that we can attain God's level of perfection.  Conversely, Protestants have typically argued that the existence of supererogatory acts would suggest that it is possible to exceed God's moral requirements and, by implication, that it is therefore possible to fulfill God's moral requirements.

Some more food for thought:  

1) Catholics often note that Paul advises that it is better to be unmarried but not wrong to get married (1 Cor 7).

2) Moses and other prophets frequently intercede with God on Israel's behalf, begging God not to bring harm unfaithful Israel when God would otherwise destroy them.  What is Moses had said "yes" to God out of obedience?  Surely, we couldn't fault Moses for obeying and deferring to God, but surely it is also good (indeed, quite heroic!) to stand before God and make the case to save Israel.

3) Can anything really be thought of as supererogatory in light of a savior who took up death upon the cross out of obedience, which implies a command (Phil 2:8)? If even the greatest act of compassion is an act of obedience to God, what else could possibly exceed "mere" obedience to God?

4) While I'm not typically Kantian on ethics, it's worth noting the question posed by the Categorical Imperative:  "What would the world look like if everyone acted like this?"  To that point, mandating supererogatory acts can create significant problems.  For example, proponents of supererogation would count giving away all of your possessions as supererogatory.  Yet, if everyone were required to do this, it would be unsustainable.  Half of us would give up our possessions to the other half, but in order to be morally upright, that other half would now have to give it back, and at the end of the matter, we'd probably have to destroy all of our possessions, whereupon we'd all die of starvation and exposure, and that's definitely not a moral good.  In such a world, giving to someone would oblige that person to give to someone else with no morally justifiable end recipient.  Giving would thus cease to be praiseworthy, since it would become a matter of divesting our material guilt onto others and forcing them into a conundrum that has no morally valid resolution.