Infinitely many composites n with n+1 dividing σ⁺(n)

Determine whether there exist infinitely many positive composite integers n such that n+1 divides σ⁺(n), where σ⁺(n)=∏_{p\mid n}(σ(p^{v_p(n)})+1).

Background

Following negative results for specific factorizations and extensive computation with no examples found up to 10^5, the authors ask about the infinitude of composite integers n satisfying the divisibility n+1 | σ⁺(n). This extends Open question 2 from existence to infinitude.