We test if cooperation is promoted by rank-order competition between groups in which all groups can be ranked first, i.e. when everyone can be a winner. This type of rank-order competition has the advantage that it can eliminate the negative externality a group's performance imposes on other groups. However, it has the disadvantage that incentives to outperform others are absent if groups perform at the same level and it therefore does not eliminate low-cooperation equilibria. We find that all-can-win competition produces a universal increase in cooperation and benefits a majority of individuals if incentives to compete are strong.