Historically, there hasn't been, it seems, any significant objections to the ontological argument on behalf of the trinity. The trinity-being is almost never mentioned, in accounts of the ontological argument. See for example the section on the ontological argument in the Catholic Encyclopedia where the trinity is not mentioned. The ontological argument has been indeed often rejected by christian theologians, following the philosophical objections of Thomas Aquinas (see the above link), but those objections were not related to the trinity.
From a logical point of view, I also don't see any special conflict between the ontological argument and the trinity.
What happens when we add the attribute of being a trinity to the "proven" supremely perfect god? That attribute either enhances his perfection, which would be a contradiction; or it reduces his perfection, which would make the proof invalid; or it is irrelevant for his state of perfection.
But there is no need to "add" the attribute of being a trinity to God, if God already possesses this attribute. The ontological argument is silent about which are the perfections that God possesses, except about one perfection: existence. One option is that God possesses trinity-being accidentally, not even as a perfection. Another option is that trinity-being is a perfection. Would this last option be a problem?
One might say that being-trinity is a "complication", that it is "not simple", etc. But is it? One might compare God to a perfect circle, or a perfect sphere. But this last analogy seems stretched, because God is not a geometrical figure. He is, rather, a god. So the relevant question would be what would a simple god (and not a simple geometrical shape) be like? And there are already many "complications" about god without the trinity, such as: how can a god be angry, of content? How can he possess a will? And many others. So that being-trinity is just one more complication among many. And if you believe, like a christian, that it is an unavoidable complication, then it doesn't conflict with the maximum simplicity that a god can have.
Furthermore, it does not seem to me apt to associate the simplicity of God specifically with the ontological argument. The ontological argument depicts God as a multiplicity, not as a unity. The argument speaks on many perfections. It speaks about God having all the perfections. It deals with many, different, perfections, and not with one, simple, perfection. So there is no apparent connection between the ontological argument, specifically, and the supposed simplicity of God.