The phrase "many magnitudes" is correct and usable in written English.
It is often used to describe a large difference in size, importance, or value. For example: The impact of this decision will be felt many magnitudes greater than the decisions that came before it.
The Nicholas brothers were many, many magnitudes better than anybody else.
In his early 20s, Travolta was, by many magnitudes, the biggest star on earth.
Inevitably given his far higher profile around the world, Hughes' passing attracted many magnitudes more attention from the press.
Antibody-based anti-TNF therapeutics (for example, adalimumab) are less conducive for animal models, because their affinities for mouse TNF are many magnitudes lower than for human TNF33.
These were limited to only a few institutions until microprocessors were developed increasing computation speed and expanding memory capacity by many magnitudes.
Now, many magnitudes that appear in contemporary physical theories are vector-valued, let that be the case with this example.
The July mainshock had a significant aftershock sequence that persisted into July and August with many magnitude 5+ events with intensities of V (Moderate) to VII (Very Strong).
However, in the IGF-IR rich cancer cell lines, the effects (for example, receptor phosphorylation) of IGF-I versus insulin activation are of many magnitude differences.
Moreover, since there are many perceptible magnitudes, there will be enough, qua line, to prove any theorem that involves lines.
In 2014, Oklahoma saw three times as many earthquakes magnitude 3.0 or greater than California.
By comparison, the draft during Vietnam was one order of magnitude bigger -- but the reaction to it was many orders of magnitudes more intense.
