We have proposed a new tumor sensitization and targeting (TST) framework, named in vivo computation, in our previous investigations. The problem of TST for an early and microscopic tumor is interpreted from the computational perspective with nanorobots being the "natural" computing agents, the high-risk tissue being the search space, the tumor targeted being the global optimal solution, and the tumor-triggered biological gradient field (BGF) providing the aided knowledge for fitness evaluation of nanorobots. This natural computation process can be seen as on-the-fly path planning for nanorobot swarms with an unknown target position, which is different from the traditional path planning methods. Our previous works are focusing on the TST for a solitary lesion, where we proposed the weak priority evolution strategy (WP-ES) to adapt to the actuating mode of the homogeneous magnetic field used in the state-of-the-art nanorobotic platforms, and some in vitro validations were performed. In this paper, we focus on the problem of TST for multifocal tumors, which can be seen as a multimodal optimization problem for the "natural" computation. To overcome this issue, we propose a sequential targeting strategy (Se-TS) to complete TST for the multiple lesions with the assistance of nanorobot swarms, which are maneuvered by the external actuating and tracking devices according to the WP-ES. The Se-TS is used to modify the BGF landscape after a tumor is detected by a nanorobot swarm with the gathered BGF information around the detected tumor. Next, another nanorobot swarm will be employed to find the second tumor according to the modified BGF landscape without being misguided to the previous one. In this way, all the tumor lesions will be detected one by one. In other words, the paths of nanorobots to find the targets can be generated successively with the sequential modification of the BGF landscape. To demonstrate the effectiveness of the proposed Se-TS, we perform comprehensive simulation studies by enhancing the WP-ES based swarm intelligence algorithms using this strategy considering the realistic in-body constraints. The performance is compared against that of the "brute-force" search, which corresponds to the traditional systemic tumor targeting, and also against that of the standard swarm intelligence algorithms from the algorithmic perspective. Furthermore, some in vitro experiments are performed by using Janus microparticles as magnetic nanorobots, a two-dimensional microchannel network as the human vasculature, and a magnetic nanorobotic control system as the external actuating and tracking system. Results from the in silico simulations and in vitro experiments verify the effectiveness of the proposed Se-TS for two representative BGF landscapes.