Competing adverbs are provided in this article. The words listed here are commonly found along with the verb competing in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb COMPETING.
actively, actually
constantly, directly
effectively, fiercely
possibly, potentially
previously, really
successfully
Hope this word list had the competing adverb you were looking for. In addition to adverbs used with competing, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.