Laser feedback-based self-mixing interferometry (SMI) has been demonstrated for diverse metric sensing applications. Typically, SMI sensors are based on such laser diodes (LDs) which provide mono-modal emission resulting in SMI signals in which each interferometric fringe occurs due to change in optical path length of λ/2, where λ is emission wavelength. However, in case multiple laser modes undergo SMI, then each mode contributes its own set of fringes. As LDs can emit multiple modes under variable operating conditions, so, non-detection of multiple SMI modes can cause drastic increase in measurement error due to wrong interpretation of fringes. Previously, the detection of multiple laser modes undergoing SMI was achieved by adding spectroscopic instruments to the SMI set-up. This, however, compromises the inherent simplicity of SMI sensing. In this paper, an automatic SMI-based multi-modality detection method is proposed which is able to detect if multiple modes of deployed LD are undergoing SMI and are contributing additional fringes within the SMI signal under variable sensing conditions. Such detection enables correct interpretation of SMI fringe count and can be used to signal occurrence of mode-hopping or secondary mode excitation. The method uses an artificial neural network, able to automatically identify uni-, bi-, or tri-modal SMI signals. Two different LDs (emitting at 637 and 650 nm) were used to acquire 131 experimental uni-, bi-, and tri-modal SMI signals for variable operating conditions and target vibration amplitude. The proposed system has achieved modality detection accuracy of 98.57% on 70 unseen experimental SMI signals.