The phrase "by/from all accounts" refers to information that has been received from multiple sources. There are many synonyms that can be used in place of this phrase, including "according to reports," "as per sources," and "based on evidence." Other options include "from what we've heard," "as far as we know," and "by all indications." Each of these phrases conveys a similar meaning, and can be used to introduce information that has been gathered from various sources. Whether you are writing a news article, a research paper, or a blog post, using synonyms for "by/from all accounts" can add variety and interest to your writing.