There are only two dispensations found in the words of scripture:
"Now if the dispensation of death, carved in letters on stone, came with such splendor that the Israelites could not look at Moses’ face because of its brightness, fading as this was, will not the dispensation of the Spirit be attended with greater splendor? For if there was splendor in the dispensation of condemnation, the dispensation of righteousness must far exceed it in splendor. "(2Cor 3:7-9 RSV)
"The law, then, engraved letter by letter upon stone, dispensed death, and yet it was inaugurated with divine splendour. That splendour, though it was soon to fade, made the face of Moses so bright that the Israelites could not gaze steadily at him. But if so, must not even greater splendour rest upon the divine dispensation of the Spirit? If splendour accompanied the dispensation under which we are condemned, how much richer in splendour must that one be under which we are acquitted!" (2 Cor 3:7-9 New English Bible)
"For, 1. The Old-Testament dispensation was the ministration of death (v. 7), whereas that of the New Testament is the ministration of life...Not only did the glory of Moses's face go away, but the glory of Moses's law is done away also; yea, the law of Moses itself is now abolished. That dispensation was only to continue for a time, and then to vanish away; whereas the gospel shall remain to the end of the world, and is always fresh and flourishing and remains glorious." Matthew Henry on 2 Cor. 3:6-11.
"The ministration of the Spirit - That is, the Christian dispensation...The ministration of condemnation - Such the Mosaic dispensation proved to all the Jews who rejected the gospel whereas through the gospel (hence called the ministration of righteousness) God both imputed and imparted righteousness to all believers." John Wesley on 2 Cor. 3:8-9
"...that great word of Jesus, 'I am not come to destroy, but to fulfill.' Had be lived to a time like ours, when the Gospel also has been embodied in a book, instead of using 'letter' and 'spirit' as mutually exclusive, he would have admitted, as we do, that both ideas apply, in some sense, to both dispensations, and that it is possible to take the old and the new alike either in the letter or in the spirit. Nevertheless, he would have been entitled to say that, if they were to be characterized in their differences, they must be characterized as he has done it: the mark of the old, as opposed to the new, is literalism, or legalism; the mark of the new, as opposed to the old, is spirituality, or freedom. They differ as law differs from life, as compulsion from inspiration. Taken thus, no one can have any difficulty in agreeing with him." The Expositor's Bible (1905) on 2 Cor. 3:4-11
"We conceive the familiar and established division to be correct, which makes two dispensations only, the Old Testament and the New. There seems no adequate reason for regarding the patriarchal age, from Adam to Moses, as essentially a different dispensation from that of Moses. Certainly that representation is incorrect which makes the former a free and gracious dispensation, while the latter only was burdened with the condemning weight of the moral and ritual law. For the moral law as to its substance, was already in force from Adam to Moses."
and again
"And first, we urge the general consideration that the Bible never speaks of more than two Covenants: that of the Law, or Works and that of Grace. The dispensations also are but two, 'the first and the second,' the 'new and the old.' But if Moses’ dispensation was a legal one in essence, then we must have three, for Abraham’s was doubtless a gracious one. We add, that there are but two imaginable ways and but two known to Scripture; 'grace' and 'works,' by which a soul can win adoption of life." Robert L Dabney, Systematic Theology
More than two dispensations can be found in man's notes, not in the Bible!
"Now if the dispensation of death, carved in letters on stone, came with such splendor that the Israelites could not look at Moses’ face because of its brightness, fading as this was, will not the dispensation of the Spirit be attended with greater splendor? For if there was splendor in the dispensation of condemnation, the dispensation of righteousness must far exceed it in splendor. "(2Cor 3:7-9 RSV)
"The law, then, engraved letter by letter upon stone, dispensed death, and yet it was inaugurated with divine splendour. That splendour, though it was soon to fade, made the face of Moses so bright that the Israelites could not gaze steadily at him. But if so, must not even greater splendour rest upon the divine dispensation of the Spirit? If splendour accompanied the dispensation under which we are condemned, how much richer in splendour must that one be under which we are acquitted!" (2 Cor 3:7-9 New English Bible)
"For, 1. The Old-Testament dispensation was the ministration of death (v. 7), whereas that of the New Testament is the ministration of life...Not only did the glory of Moses's face go away, but the glory of Moses's law is done away also; yea, the law of Moses itself is now abolished. That dispensation was only to continue for a time, and then to vanish away; whereas the gospel shall remain to the end of the world, and is always fresh and flourishing and remains glorious." Matthew Henry on 2 Cor. 3:6-11.
"The ministration of the Spirit - That is, the Christian dispensation...The ministration of condemnation - Such the Mosaic dispensation proved to all the Jews who rejected the gospel whereas through the gospel (hence called the ministration of righteousness) God both imputed and imparted righteousness to all believers." John Wesley on 2 Cor. 3:8-9
"...that great word of Jesus, 'I am not come to destroy, but to fulfill.' Had be lived to a time like ours, when the Gospel also has been embodied in a book, instead of using 'letter' and 'spirit' as mutually exclusive, he would have admitted, as we do, that both ideas apply, in some sense, to both dispensations, and that it is possible to take the old and the new alike either in the letter or in the spirit. Nevertheless, he would have been entitled to say that, if they were to be characterized in their differences, they must be characterized as he has done it: the mark of the old, as opposed to the new, is literalism, or legalism; the mark of the new, as opposed to the old, is spirituality, or freedom. They differ as law differs from life, as compulsion from inspiration. Taken thus, no one can have any difficulty in agreeing with him." The Expositor's Bible (1905) on 2 Cor. 3:4-11
"We conceive the familiar and established division to be correct, which makes two dispensations only, the Old Testament and the New. There seems no adequate reason for regarding the patriarchal age, from Adam to Moses, as essentially a different dispensation from that of Moses. Certainly that representation is incorrect which makes the former a free and gracious dispensation, while the latter only was burdened with the condemning weight of the moral and ritual law. For the moral law as to its substance, was already in force from Adam to Moses."
and again
"And first, we urge the general consideration that the Bible never speaks of more than two Covenants: that of the Law, or Works and that of Grace. The dispensations also are but two, 'the first and the second,' the 'new and the old.' But if Moses’ dispensation was a legal one in essence, then we must have three, for Abraham’s was doubtless a gracious one. We add, that there are but two imaginable ways and but two known to Scripture; 'grace' and 'works,' by which a soul can win adoption of life." Robert L Dabney, Systematic Theology
More than two dispensations can be found in man's notes, not in the Bible!