Rapid Serial Visual Presentation (RSVP)-based Brain-Computer Interfaces (BCIs) facilitate high-throughput target image detection by identifying event-related potentials (ERPs) evoked in EEG signals. The RSVP-BCI systems effectively detect single-class targets within a stream of images but have limited applicability in scenarios that require detecting multiple target categories. Multi-class RSVP-BCI systems address this limitation by simultaneously identifying the presence of a target and distinguishing its category. However, existing multi-class RSVP decoding algorithms predominantly rely on single-modality EEG decoding, which restricts their performance improvement due to the high similarity between ERPs evoked by different target categories. In this work, we introduce eye movement (EM) modality into multi-class RSVP decoding and explore EEG and EM fusion to enhance decoding performance. First, we design three independent multi-class target RSVP tasks and build an open-source dataset comprising EEG and EM signals from 43 subjects. Then, we propose the Multi-class Target RSVP EEG and EM fusion Network (MTREE-Net) to enhance multi-class RSVP decoding. Specifically, a dual-complementary module is proposed to strengthen the differentiation of uni-modal features across categories. To improve multi-modal fusion performance, we adopt a dynamic reweighting fusion strategy guided by theoretically derived modality contribution ratios. Furthermore, we reduce the misclassification of non-target samples through knowledge transfer between two hierarchical classifiers. Extensive experiments demonstrate the feasibility of integrating EM signals into multi-class RSVP decoding and highlight the superior performance of MTREE-Net compared to existing RSVP decoding methods. The proposed MTREE-Net and open-source dataset provide a promising framework for developing practical multi-class RSVP-BCI systems.