The phrase "almost limitless number of" is correct and usable in written English.
It can be used when describing a very large quantity that is not entirely infinite but is still extremely high.
Example: "The universe contains an almost limitless number of stars, far beyond what we can see with the naked eye."
Alternatives: "virtually infinite number of" or "nearly endless number of".
Thus, by incorporating foreign DNA (for example, a mammalian gene) into a bacterium, researchers can obtain an almost limitless number of copies of the inserted gene.
Collectively B cells recognize an almost limitless number of antigens; however, individually each B cell can bind to only one type of antigen.
Instead of being starved for space, he had the opposite problem -- cleaning, painting, furnishing and finding new purposes for an almost limitless number of once-stultifying cubicles.
The exquisite design of CaM allows it to assume an almost limitless number of conformations, each one dictated by the amino acid sequence of the CaM-binding domain of the individual target proteins.
There are only two ingredients, which must be combined and then separated, but somehow these variables can produce an almost limitless number of errors and misjudgments, any one of which can smother the flavors.
During the 19th century there developed the idea of a limited number of elements, each consisting of a particular type of atom, that could combine in an almost limitless number of ways to form chemical compounds.
By so doing, Andronicus III and Cantacuzenus were able to call on the services of almost limitless numbers of Turkish soldiers to fight for them against their other enemies: the Italians in the Aegean islands and the Serbs and the Bulgars in Macedonia and Thrace.
(One could argue that, because of their existing ability to import almost limitless numbers of international students and postdocs, they are visa mills already).
"There are a limitless number of objects, in every corner of the universe.
Eliminating the object has opened a seemingly limitless number of possibilities for Sehgal.
The learners today have access to a limitless number of visuals, many inaccessible until recently.
