It is evident from scriptures that multiple ansavatharas of Vishnu existed at same time may or may not be along with his purnavathar.
But did Vishnu ever appear as two or more purnavatharas at the same time?
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Our holy scriptures are not uaninimous about who is Poorna Avatara.In the Ist canto of Srimadbhagavatam (1/3/28), we get all Avataras are angsha or kala but Sri Krishna is Swayam Bhagavan. But in 10/89/59-60, when Sri Krishna goes to rescue the life of a brahmin son with Arjuna to the highest loka, they find Sri Bhagavan lying in anantasyya,Who tells Sri Krishna that both He and Arjuna are actually His 'part' or 'kala' incarnations. In the Mahabharat,(Moksha parva, chapter 180), Bhishma says that Sri Krishna has been born as one eighth part of the Godhead Brahman.
In Anandaramayana,(Saarkanda, sarga 3), both Rama and Krishna are mentioned as Purnavataras, Rama being the most glorious one. In Vrihat Parasara Hora, Rama, Krishna, Nrisimha and Varaha are depicted as Purna avataras. Rest are mentioned as having jivamsasa. In Brahmavaaivartapurana,(chapter 116), we again get that Krishna is swayam Bhagavan, but Sri Rama has more glory. But He was unaware of the Self because of the curse of Brahmaa.(Reference: PranavaPrema Pijusha Bhashya of Gita by Sri Sitaramdas Omkarnath, vol 2).
So if it can not be known with certainty who is Purna Avatara, who is Amsa Avatara and Who is Swayam Bhagavan, this question has no answer.