Context : S stars are late-type giants with overabundances of s-process elements . They come in two flavours depending on the presence or not of technetium ( Tc ) , an element without stable isotopes . Intrinsic S stars are Tc-rich and genuine asymptotic giant branch ( AGB ) stars while extrinsic S stars owe their s-process overabundances to the pollution from a former AGB companion , now a white dwarf ( WD ) . In addition to Tc , another distinctive feature between intrinsic and extrinsic S stars is the overabundance of niobium ( Nb ) in the latter class . Indeed , since the mass transfer occurred long ago , ^ { 93 } Zr had time to decay into the only stable isotope of Nb , ^ { 93 } Nb , causing its overabundance . Aims : We discuss the case of the S stars BD+79 ^ { \circ } 156 and o ^ { 1 } Ori whose specificity is to share the distinctive features of both intrinsic and extrinsic S stars , namely the presence of Tc along with a Nb overabundance . Methods : We used high-resolution HERMES optical spectra , MARCS model atmospheres of S stars , Gaia DR2 parallaxes and STAREVOL evolutionary tracks to determine the stellar parameters and chemical abundances of the two S stars , and to locate them in the Hertzsprung-Russell ( HR ) diagram . Results : BD+79 ^ { \circ } 156 is the first clear case of a bitrinsic star , i.e . a doubly s-process-enriched object , first through mass transfer in a binary system , and then through internal nucleosynthesis ( responsible for the Tc-enrichment in BD+79 ^ { \circ } 156 which must therefore have reached the AGB phase of its evolution ) . This hybrid nature of the s-process pattern in BD+79 ^ { \circ } 156 is supported by its binary nature and its location in the HR diagram just beyond the onset of the third dredge-up on the AGB . The Tc-rich , binary S-star o ^ { 1 } Ori with a WD companion was another long-standing candidate for a similar hybrid s-process enrichment . However the marginal overabundance of Nb derived in o ^ { 1 } Ori does not allow to trace unambiguously the evidence of a large pollution coming from the AGB progenitor of its current WD companion . As a side product , the current study offers a new way of detecting binary AGB stars with WD companions by identifying their Tc-rich nature along with a Nb overabundance . Conclusions :