In a single-input single-output (SISO) linear time-invariant (LTI) feedback control setting with a loop delay τ, unstable poles of the finite-dimensional plant being controlled pose significant limitation on the delay margin τ̅ of the closed loop system. An analytical study recently published derived conditions on the upper-bound τ* of this delay margin for certain unstable plant transfer functions; a derivation that holds independent of proper finite-dimensional stable controllers that can be proposed [1]. This inherent limitation posed by the plant unstable poles therefore does not allow stabilizing the loop for a given delay value τ' > τ* no matter what the controller is. A remedy to this as demonstrated in this article as the main contribution is to pursue a numerical optimization scheme to design two disjoint stable delay intervals [0, h₁) and (h₂, h₃) with 0 <; h₁ <; h₂ <; h₃, whereby it is possible to design h₂ and h₃ such that τ' ∈ (h₂; h₃) and hence the closed-loop can be made stable for τ = τ' > τ*.