Constructing adverbs are provided in this article. The words listed here are commonly found along with the verb constructing in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb CONSTRUCTING.
actively, actually
busily, carefully
simultaneously, socially
Hope this word list had the constructing adverb you were looking for. In addition to adverbs used with constructing, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.