The paper provides a comprehensive analytical and numerical examination of the properties of single-domain superparamagnetic magnetite nanoparticles, aiming to devise strategies for selectively damaging the membranes of malignant cells and enhancing anticancer magnetomechanical therapy. It highlights the potential formation of anisotropic aggregates composed of multiple magnetite nanoparticles even in the absence of an external magnetic field. These aggregates, when combined with gold nanoparticles, can selectively bind to mechanoreceptors on the membranes of malignant cells employing aptamers. The aggregation process suppresses thermal fluctuations of the intrinsic magnetic moments of individual particles, thanks to the collective magnetic field generated by the resulting subaggregates. As a result, these nanoparticle aggregates demonstrate stabilization of their total magnetic moment driven by this cooperative behavior. The growth of aggregates of magnetic nanoparticles is accompanied by an increase in the total magnetic moment of the aggregates and the strength of the mechanical effect on cell mechanoreceptors. This enhanced interaction can contribute to the programmed death of malignant cells (apoptosis) in malignant cells when exposed to an alternating magnetic field. The analysis presented makes it possible to explain the experimental results from magnetomechanical therapy utilizing gold and magnetite nanoparticles, which effectively suppresses Ehrlich carcinoma both in vivo and in vitro within an alternating magnetic field. These results affirm the promising potential for implementing this method as a highly effective treatment for malignant tumors.