The Oriental Orthodox communion do not consider the latter 4 councils to be ecumenical - and you would need to define exactly what you mean. But they reject all of the heresies that these latter councils reject. Indeed having never abandoned the veneration of icons or ever having considered the Three Chapters as anything but blasphemy they did not need a council to declare these things.
The Oriental Orthodox have always and at all times condemned any heresy which diminishes the confession of the union of a perfect humanity and a perfect divinity in Christ. Eutyches was condemned from the time of Chalcedon through to the present and any who taught his heresy were excommunicated.
A very recent and official repetition of this position says:
"We agree in condemning the Nestorian and the Eutychian heresies. We neither separate nor divide the human nature in Christ from His divine nature, nor do we think that the former was absorbed in the latter and thus ceased to exist.
The four adverbs used to qualify the mystery of the hypostatic union belong to our common tradition - without commingling (or confusion) (asyngchytos), without change (atreptos), without separation (achoristos) and without division (adiairetos). Those among us who speak of two natures in Christ, do not thereby deny their inseparable, indivisible union; those among us who speak of one united divine-human nature in Christ do not thereby deny the continuing dynamic presence in Christ of the divine and the human, without change, without confusion."
"Both families agree in condemning the Eutychian heresy. Both families confess that the Logos, the Second Person of the Holy Trinity, only begotten of the Father before the ages and consubstantial with Him, was incarnate and was born from the Virgin Mary Theotokos; fully consubstantial with us, perfect man with soul, body and mind (nouj); He was crucified, died, was buried, and rose from the dead on the third day, ascended to the Heavenly Father, where He sits on the right hand of the Father as Lord of all Creation. At Pentecost, by the coming of the Holy Spirit He manifested the Church as His Body. We look forward to His coming again in the fullness of His glory, according to the Scriptures."
"Both families agree that the natures with their proper energies and wills are united hypostatically and naturally without confusion, without change, without division and without separation, and that they are distinguished in thought alone."
And of course through the course of history I could pull out hundreds and hundreds of similar statements.
The non-Chalcedonians did not reject Chalcedon because they supported Eutyches but because they believed that Chalcedon gave room for Nestorianism to continue to flourish.