Can a person become a buddha after reaching nirvana?

Maybe? It becomes a little confusing trying to reconcile the Therevada four path model and the Mahayana bhumi model. The individual, after directly apprehending nibbana (becoming a stream-winner in the Therevada model), would just have to become a fully, self enlightened buddha within seven life times. One problem though is how can they be said to be fully self enlightened if they attained to a stage of enlightenment through a previous buddha's teachings.

If you are talking about parinibbana then it seems to go against the Therevada understanding to say that one could enter into parinibbana and then later be reborn in order to become a buddha.

The way you phrased this question though "So after he enters nirvana he can't accomplish what he wants to accomplish?" Implies that the individual won't be able to enter into parinibbana - since parinibbana is based on being free from wanting. By wanting to do other things the mind will incline toward a rebirth that allows for the fulfillment of those wants.

I would think that someone who has taken the bodhisattva vow and truly aspires toward that goal would not be able to directly apprehend nibbana until their final human life. Subsequently becoming a fully, self enlightened buddha.

There are two ways to reach Nirvana: the way of limitation and the way of total acceptance.

In the way of limitation, you simplify one's life to basically turn it into a controlled meditation environment. You live far from people, with few possessions, you don't watch TV, don't participate in projects - and in all these ways you minimize the chance of conflict between "should" and "is".

The Nirvana of total acceptance is when you open your mind, get rid of ego, and become completely transparent, so that you can live in the middle of civilization, do everything people do, and still have a mind with no conflict.

In Mahayana we say that the first type of Nirvana is temporary. At some point you understand this as limitation of your mind, an attachment. Then you exit that Nirvana and start training on the path of acceptance in the middle of people and without stopping all activities.

When you complete this second training, you achieve the second type of Nirvana. Doesn't mean you are Buddha yet, because to be Buddha you need to learn how to enlighten all different types of people. Luckily with this type of Nirvana you can keep working with people. Then after many many lives of training like that, someone is born and using all those previous lives as foundation quickly becomes Buddha.

P.S. To address user70's doubt about *self-*enlightenment, there's still taking advantage of all the hard work performed in previous lives on the basis of teachings of previous Buddha, it's not like new Buddha grows from zero in complete isolation. But the "self-" part comes in the form that in one life Buddha figures it out all by himself, no one explains it to him, no one trains him. He just gets bits and pieces here and there and very quickly assembles the puzzle all by himself.

Theravada answer for this depends on what do you mean by buddha. If you mean Samma Sambuddha, yes there can be only one for a very long period of time. However in therawada tradition all fully enligtened beings are buddhas.

Aharaths are callsd Shrawaka buddha as he/she become enligtened by followig teaching discovered by another samma sambuddha.

Either way thee is no more mission after fully enlightned.

No! Once you attain Nibbana, mission is accomplished. There are no more ambitions. So it is technically not possible. It's like getting the PhD vs getting the PhD with highest honors. But once you get it, it's done.

According to Mahayana, a person can become a buddha after reaching nirvana. We hold that all sentient beings will, sooner or later, become buddhas - be it after they reached nirvana or not.

As to the hearers and solitary realizers, we say that while they dwell in abiding nirvana, the buddhas manifest to them and encourage them to enter the Mahayana path, so that they will in turn become buddha - thereby achieving their own benefits completely, and the benefits of others. This is the presentation of the Abhisamaya-Alamkara:

The arhat without the contaminated aggregates will hear the voice of the Buddha telling him or her something like “you are free from the suffering of samsara, but still you have not gained nonabiding nirvana. Therefore, you need to enter the Mahayana path.” With these words the Buddha wakes up the arhat from their blissful meditative state.

In this context, there are two types of nirvana:

1. Abiding nirvana. It is the nirvana of hearers and solitary realizers. We refer to it, in a somehow derogatory fashion, as "individual liberation".
2. Non-abiding nirvana. It is the final true cessation, the nirvana that bodhisattvas attain when they achieve full perfect enlightenment - the path of no more learning.

In his commentary to Bodhisattvacharyāvatāra Geshe Gyaltsen said:

Non-abiding, the nirvana of a buddha, is a nirvana not abiding in the two extremes. It is not the nirvana of a hearer or solitary realizer, but the nirvana of the highest state of development of a buddha.

The following passage also shows that the one who has attained abiding nirvana did not abandon all objects of abandonment.

Abiding nirvana is a temporal goal. Temporal has the connotation of being ordinary. This is because there is still something to abandon. But it is tricky because the term 'nirvana' is also synonymous with '[final] true cessation'. And the true cessation of a buddha is not something that is ordinary.

There are buddhas who did not enter abiding nirvana, but buddhahood is non-abiding nirvana. After a bodhisattva enters non-abiding nirvana, he abides in neither of the two extremes of peace (abiding nirvana) or samsara. This is because here, samsara is understood as the contaminated aggregates. A buddha is free from contaminated aggregates, and he can manifest countless enjoyment body and emanation bodies. For instance, we say that an already enlightened one showed the aspect of being born as Shakyamuni, and then showed the aspect of undergoing austerities and achieving enlightenment while he was, in fact, already enlightened. We say that Shakyamuni buddha was a supreme emanation body, one of the countless bodies a buddha can emanate so as to benefit sentient beings.