Researchers affiliated with multiple institutions are increasingly seen in current scientific environment. In this paper we systematically analyze the multi-affiliated authorship and its effect on citation impact, with focus on the scientific output of research collaboration. By considering the nationality of each institutions, we further differentiate the national multi-affiliated authorship and international multi-affiliated authorship and reveal their different patterns across disciplines and countries. We observe a large share of publications with multi-affiliated authorship (45.6%) in research collaboration, with a larger share of publications containing national multi-affiliated authorship in medicine related and biology related disciplines, and a larger share of publications containing international type in Space Science, Physics and Geosciences. To a country-based view, we distinguish between domestic and foreign multi-affiliated authorship to a specific country. Taking G7 and BRICS countries as samples from different S&T level, we find that the domestic national multi-affiliated authorship relate to more on citation impact for most disciplines of G7 countries, while domestic international multi-affiliated authorships are more positively influential for most BRICS countries.