A tissue infiltration apparatus (1) for specimens present in cassettes (5) comprises at least two liquid containers (7, 11, 13, 15) and a transport apparatus (6). Multiple cassettes (5) are receivable in a transport basket (4). The transport apparatus (6) is configured in such a way that at least two transport baskets (4) are transportable in the tissue infiltration apparatus (1). A transport basket (4) is deliverable to, and/or movable away from, a liquid container (7, 11, 13, 15) with the transport apparatus (6). An execution sequence (21) in which the transport baskets (4) pass through the liquid containers (7, 11, 13, 15) is definable. To enable accelerated or preferred processing of a transport basket (4) with the tissue infiltration apparatus (1), at least one means (8) is provided with which the order of two transport baskets (4) is definably modifiable.