double-handshake clasp
Refers to where ya grasp da "inside" hands of a couple in your hands, so dat your left and right hands are fully fitted into their corresponding hands, rather than just employing either classic holding-hands clasps or finger-interlacings with their "outside" hands, which would allow them to still hold hands wif each other while they're giving your hands some warm lovies wif their own.
Employing da double-handshake clasp can indeed be delightfully soh-shuh-buhl for all concerned; just be careful dat you don't hold those two hands for so long a time dat you start engaging in inside-hands hogging. If you wanna hold hands wif them for extended periods, smilingly fit their inside hands back into a classic hands-holding clasp after maybe half a minute of holding them yourself, and then take their free outside hands to hold instead.