Completing adverbs are provided in this article. The words listed here are commonly found along with the verb completing in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb COMPLETING.
actually, currently
finally, fully
simply, successfully
Hope this word list had the completing adverb you were looking for. In addition to adverbs used with completing, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.