Many fields face an increasing prevalence of multi-authorship, and this poses challenges in assessing citation metrics. Here, we explore multiple citation indicators that address total impact (number of citations, Hirsch H index [H]), co-authorship adjustment (Schreiber Hm index [Hm]), and author order (total citations to papers as single; single or first; or single, first, or last author). We demonstrate the correlation patterns between these indicators across 84,116 scientists (those among the top 30,000 for impact in a single year [2013] in at least one of these indicators) and separately across 12 scientific fields. Correlation patterns vary across these 12 fields. In physics, total citations are highly negatively correlated with indicators of co-authorship adjustment and of author order, while in other sciences the negative correlation is seen only for total citation impact and citations to papers as single author. We propose a composite score that sums standardized values of these six log-transformed indicators. Of the 1,000 top-ranked scientists with the composite score, only 322 are in the top 1,000 based on total citations. Many Nobel laureates and other extremely influential scientists rank among the top-1,000 with the composite indicator, but would rank much lower based on total citations. Conversely, many of the top 1,000 authors on total citations have had no single/first/last-authored cited paper. More Nobel laureates of 2011-2015 are among the top authors when authors are ranked by the composite score than by total citations, H index, or Hm index; 40/47 of these laureates are among the top 30,000 by at least one of the six indicators. We also explore the sensitivity of indicators to self-citation and alphabetic ordering of authors in papers across different scientific fields. Multiple indicators and their composite may give a more comprehensive picture of impact, although no citation indicator, single or composite, can be expected to select all the best scientists.