A universal multi-parameter sensing scheme based on a self-interference micro-ring resonator (SIMRR) is proposed. Benefit from the special intensity sensing mechanism, the SIMRR allows multimode sensing in a wide range of wavelengths but immune from frequency noise. To process the multiple mode spectra that are dependent on multiple parameters, we adopt the machine learning algorithm instead of massive asymptotic solutions of resonators. Employing the proposed multi-mode sensing approach, a two-parameter SIMRR sensor is designed. Assuming that two gases have different wavelength dependence of refractive indices, the feasibility and effectiveness of the two-parameter sensing strategy are verified numerically. Moreover, the dependence of parameter estimation accuracy on the laser intensity noises is also investigated. The numerical results indicate that our scheme of multi-parameter sensing in a multimode SIMRR holds great potential for practical high-sensitive sensing platforms compared with the single-mode sensing based on whispering gallery mode (WGM) resonators.