Targeting of pre-mRNA by short splice-switching oligonucleotides (SSOs) is increasingly being used as a therapeutic modality, one rationale being to disrupt splicing so as to remove exons containing premature termination codons, or to restore the translation reading frame around out-of-frame deletion mutations. The aim of this study was to investigate the effect of chemically linking individual SSOs so as to ascertain equimolar cellular uptake that would provide for more defined drug formulations. In contrast to conventional bispecific SSOs generated by conjugation in solution, here we describe a protocol for synthesis of bispecific SSOs on solid phase. These SSOs comprised of either a non-cleavable hydrocarbon linker or disulfide-based cleavable linkers. To assess the efficacy of these SSOs we have utilized splice switching to bypass a disease-causing mutation in the DMD gene concurrent with disruption of the reading frame of the myostatin gene (Mstn). The premise of this approach is that disruption of myostatin expression is known to induce muscle hypertrophy and so for Duchenne muscular dystrophy (DMD) could be expected to have a better outcome than dystrophin restoration alone. All tested SSOs mediated simultaneous robust exon removal from mature Dmd and Mstn transcripts in myotubes. Our results also demonstrate that using cleavable SSOs is preferred over the non-cleavable counterparts and that these are equally efficient at inducing exon skipping as cocktails of monospecific versions. In conclusion, we have developed a protocol for solid-phase synthesis of single molecule cleavable bispecific SSOs that can be efficiently exploited for targeting of multiple RNA transcripts.