  The presence of a thermodynamic phase of a three-stranded DNA, namely, a
mixed phase of bubbles of two bound strands and a single one, is established
for large dimensions ($d\geq 5$) by using exact real space renormalization
group (RG) transformations and exact computations of specific heat for finite
length chains. Similar exact computations for the fractal Sierpinski gasket of
dimension $d<2$ establish the stability of the phase in presence of repulsive
three chain interaction. In contrast to the Efimov DNA, where three strands are
bound though no two are bound, the mixed phase appears on the bound side of the
two chain melting temperature. Both the Efimov-DNA and the mixed phase are
formed due to strand exchange mechanism.
