Biosimilars are medical products that are developed as copies of already established, large molecule drugs (biologics). For gaining approval, sponsors have to conrm that the proposed biosimilar has the same efficacy and safety as the originator product. This comparability exercise includes also, in most cases, that large clinical trials are conducted in patients. However, even with the evidence gained during the clinical studies, there is still some uncertainty if patients who were already treated with the originator can be switched to the biosimilar or if even multiple switches between the biosimilar and the originator are acceptable. A simple way to address the question of switchability is the estimation of so-called mixed and self-carryover effects, which are carryover effects that not only depend on the treatment in the current period, but also on the treatment in the previous period. In this paper, we determine universally optimal designs for the estimation of mixed-carryover effects in a linear model with treatment, period, subject and self-carryover as nuisance parameters.