## 1 Introduction  
In general, the trapped modes or TMs are protected eigenmodes of ideal lossless optical systems, which are characterized by high quality factors [1, 2] and detected via narrow features in the reflection/transmission spectra. Such states can be obtained by symmetry breaking for either individual building blocks or the entire lattice [3, 4]. In particular, nanoparticles (NPs) with broken symmetry of the shape can support a bianisotropic response, for which an incident wave that even normally propagates to the nanoparticle's base can excite dipole components in the nanoparticle that are longitudinal to its wave vector [5]. By choosing the period of lattice composed of such bianisotropic building blocks, it is possible to synchronize the phases of the dipoles of individual NPs, which results in the formation of the TM on the metasurface. At the same time, introducing defects into the metasurface's structure leads to the opening of a channel for energy leakage from the TM and, hence, to the decrease in its quality factor, and such a mode is called a quasi-trapped mode (QTM). In the case where the building blocks of the metasurface are made of high-anisotropic materials, among other possibilities such as the control of their shape [6] and chemical composition [7], an additional degree of freedom arises, allowing one to control the spectral position of the QTM, as well as its characteristics [8]. The bulk transition metal dichalcogenides (TMDCs) are good candidates to be used as such materials because they possess a unique combination of high refractive index [9] and strong optical anisotropy [10]. The first feature allows one to observe the bright Mie resonances in the visible and near infrared ranges for nanoparticles fabricated from such a material [9; 11]. The second one determines the large birefringence, which can be used for creation of ultra-thin polarizing devices [12]. One of the remarkable features of QTMs in metasurfaces is their polarization sensitivity, when change in the polarization of the exciting field to the orthogonal one can lead, in particular, to switching between electric and magnetic type of QTM [1]. This can be used, among other applications, to design selective polarizing mirrors and optical routers [13; 14; 15; 16]. At the same time, to increase the coding density and bandwidth of such devices, it is important to realize the conditions corresponding to the excitation of several QTMs at once on the metasurface and switching between them. In this paper, we propose a strategy for design of all-dielectric metasurfaces supporting several quasi-trapped modes at close frequencies at once. Such a possibility is achieved through the use of MoS\({}_{2}\) as a material of the building blocks of the metasurface. Light scattering in MoS\({}_{2}\) material is based on the strong anisotropy of its optical properties under irradiation by light with polarization oriented along and across the layers [10]. This is due to the fact that MoS\({}_{2}\) is a layered van der Waals material and has a close packing of atoms within the layer, while individual layers are arranged at a considerable distance from each other and held by weak van der Waals forces. Exfoliated individual layers of such a material are valuable for creation of ultra-thin transistors [17], integrated circuits on flexible substrates [18], nano- and biosensors [19; 20], and photocatalytic applications [21]. At the same time, the fabrication of nanoparticles from such bulk materials [9; 22; 23; 24] leads to the appearance of wide possibilities for control of spectra and scattering patterns, light reflection, and transmission coefficients by combining and optimizing the shape of nanoparticles and orientation of material layers in them. In addition, MoS\({}_{2}\) disks possessing strong optical anisotropy can have several dipole resonances at once in a narrow range of the infrared region under lateral irradiation. This leads to the appearance of a set of features for the spectral dependences of their electric and magnetic polarizability.