Bichlmeyer suggest that this be the case, in context of hydronymy. It's good to have that on record for once, so I should quote it.
Translated freely: The past assumption of a single, unique etymology is not tennable anymore. Much rather, the situation optains for manifold hydronyms, rarer for place-names, that one can show different etymologies and must do so, which may be classifiable based of language-internal and -external factors.[1]
This is from the introduction to an investigation which concludes with three different hypotheses. The expressed sentiment is that hypothesis is sometimes as far as you get, and that the drive to go further out on a limb, because rigour would require a unique solution, is actually toxic in practice.
Discussion: It does not generalize easily for a basic answer to your question because that is actually a wicked problem.
First of all, what is a word? Different interpretations exist, and every definition might beget different etymologies for the word.
The details hardly don't matter here. It should suffice to have an authoritative opinion on record, which contrasts sharply with the neo-grammarian school (end of the 19th century).
For simplicities sake it can be argued that if words may be polysemous and homophone, the comparative method will be eventually unable to identify convergence, divergence and coincident uniquely. Instead of a hierarchical tree-model, one might have to imagine a hyper-linked web. *gasp* welcome to the 21st century.
[1] Harald Bichlmeier, Zur Etymologie der Sippe des Namens der Ruhr, pg. 154:
Die früher – und teils auch noch heute – übliche Präsentation einer ein-zigen, man könnte sagen: allein glückselig machenden Etymologie erweist sich als ein nicht mehr haltbares Konzept: Vielmehr ergibt sich v.a. für zahlreiche Gewässer-, seltener auch für Ortsnamen, die Situation, dass man mehrere Etymologien aufzeigen kann und muss, die sich dann aufgrund teils inner-sprachlicher, teils auch außersprachlicher Faktoren allenfalls als mehr oder weniger wahrscheinlich kategorisieren lassen.