There are a number of important principles involved. The most important of these, I think, is that the priest should not himself innovate and change the liturgy sponte sua. Here, I think that there is a crucial distinction to be made. On the one hand, priests might make up new elements that have never been part of the Church's liturgy - for example improvisations in the Eucharistic Prayer, saying "Bertha. The body of Christ", clown outfits, balloons etc.
On the other hand - and I believe that this is genuinely a different issue - there is the question of introducing elements that have long been part of the tradition of the Church into the newer form of the Roman rite. Here I think we can look at several different levels.
1. Elements that are perfectly consonant with the new rubrics
For example: how should you bow? Priests saying the Novus Ordo sometimes step back from the altar and make a profound bow a the "In spiritu humilitatis..." There is no direction saying what sort of bow should be made at the "Supplices te rogamus..." In such cases, a priest familiar with the rubrics of the older form could observe them at the new form without there needing to be any dispute. The older form could give direction at these points where there is none in the newer form.
2. Elements that can be introduced without disturbance
The Holy Father's saying of the prayers during the incensation of the altar is a good example. The priest can silently say the prayer "Dirigatur Domine..." without disturbing anyone. Priests with no experience of the older form would not necessarily know these prayers. But many younger priests would be glad to say them quietly.
Other examples would be: the vesting prayers before Mass, the Aufer a nobis on the way to the altar, the Oramus te when kissing the altar, the Placeat tibi during the "pausa" after communion or on the way back to the sacristy. These elements would genuinely enrich the Novus Ordo for many priests. They would also enrich the rite per accidens for the laity because of their contribution to the devotion of the priest.
3. Elements that could be fairly easily allowed
I understand that there was a proposal (defeated in the event) to allow the old offertory prayers to be said (silently, as is the first option in the Novus Ordo) . I can see no cogent reason not to allow these prayers to be said - nor to forbid the additional gestures and genuflections in the Roman Canon - another possibility that has been proposed before. Cardinal Ratzinger in "The Spirit of the Liturgy" suggested the possibility of allowing the Canon to be said silently. This would be a more significant option because of its impact on the laity who are used to hearing the Canon said out loud; but it would not take long for people to become accustomed to this way of saying the Canon.
Fr Kocik referred to the 1978 answer in Notitiae and my observation that this could lead to ridiculous consequences if interpreted strictly. (See: Is your alb back to front?) Surely, as he hints, this approach to the Novus Ordo has now been thoroughly superceded?
The key principle is that enunciated by Pope Benedict in his accompanying letter to Summorum Pontificum:
What earlier generations held as sacred, remains sacred and great for us too, and it cannot be all of a sudden entirely forbidden or even considered harmful.This principle can provide us with a key to uncovering the riches of tradition in the newer form of the Roman Rite.