We use multivariate total positivity theory to exhibit new families of peacocks. As the authors of [F. Hirsch, C. Profeta, B. Roynette and M. Yor, Peacocks and associated martingales vol. 3. Bocconi-Springer (2011)], our guiding example is the result of Carr−Ewald−Xiao [P. Carr, C.-O. Ewald and Y. Xiao, Finance Res. Lett. 5 (2008) 162–171]. We shall introduce the notion of strong conditional monotonicity. This concept is strictly more restrictive than the conditional monotonicity as defined in [F....