In our work, we show how, for a network of bosonic modes, canonical commutation relations constrain the coefficients relating input and internal modes. Based on these constraints, we derive a lower bound on the total steady‑state squeezing achievable in reservoir‑engineered (dissipative) squeezing schemes, quantified by the sum of mode-optimal quadrature variances, each normalized to its corresponding input variance. The bound on this normalized sum follows solely from canonical commutation relations and stability, and, in the strong‑coupling limit, is saturated at unity. Furthermore, we show that adding independent parametric driving terms for each mode changes the quantum noise–gain balance and yields, for the same normalized mode-optimal sum, a distinct optimum bound, approaching 1/2. In addition, we show how these constraints allow us to reformulate the Duan inseparability criterion for a three mode bosonic system in terms of a single parameter-dependent figure of merit. Our results apply directly to current electromechanical and nanomechanical experiments and indicate that the two-mode bounds can be experimentally approached even at room temperature.