nonselfadjoint) spaces of operators. These directions cover (dual) operator algebras and (dual) operator spaces, e.g. [@Ble01; @BleKas08; @BMP00; @BMN99; @Ele08; @Ele10; @Ele12; @Ele14; @EleKak16; @ElePau08; @EPT10; @Kas09]. There are two main streams in this endeavour. Blecher, Muhly and Paulsen [@BMP00] introduced a strong Morita equivalence ${\stackrel{\textup{SME}}{\thicksim}}$, along with a Morita Theorem I, where the operator algebras ${{\mathcal{A}}}$ and ${{\mathcal{B}}}$ are symmetrically decomposed by two bimodules $M$ and $N$, i.e. $${{\mathcal{A}}}\simeq M \otimes_{{\mathcal{B}}}N {\quad\text{and}\quad}{{\mathcal{B}}}\simeq N \otimes_{{\mathcal{A}}}M.$$ Morita Theorems II and III for ${\stackrel{\textup{SME}}{\thicksim}}$ were provided by Blecher [@Ble01]. On the other hand Eleftherakis [@Ele08] introduced a strong $\Delta$-equivalence ${\, \stackrel{\textup{$\Delta$}}{\thicksim} \,}$ that is given by a generalized similarity under a TRO $M$, i.e. $${{\mathcal{A}}}\simeq M \otimes {{\mathcal{B}}}\otimes M^* {\quad\text{and}\quad}{{\mathcal{B}}}\simeq M^* \otimes {{\mathcal{A}}}\otimes M.$$ Although they coincide in the case of C\*-algebras, relation ${\, \stackrel{\textup{$\Delta$}}{\thicksim} \,}$ is strictly stronger than relation ${\stackrel{\textup{SME}}{\thicksim}}$. Indeed ${\stackrel{\textup{SME}}{\thicksim}}$ does not satisfy a Morita Theorem IV, even when $X$ and $Y$ are unital [@BMP00 Example 8.2]. However a Morita Theorem IV holds for ${\, \stackrel{\textup{$\Delta$}}{\thicksim} \,}$ on $\si$-unital operator algebras [@Ele14 Theorem 3.2].

The Morita context can be modified to cover other classes as well. In their seminal paper, Muhly and Solel [@MuhSol00] introduced a strong Morita 