We predict several new exotic doubly heavy hadronic resonances, inferring from the observed exotic bottomoniumlike and charmoniumlike narrow states X(3872), Zb(10610), Zb(10650), Zc(3900), and Zc(4020/4025). We interpret the binding mechanism as mostly molecularlike isospin-exchange attraction between two heavy-light mesons in a relative S-wave state. We then generalize it to other systems containing two heavy hadrons which can couple through isospin exchange. The new predicted states include resonances in meson-meson, meson-baryon, baryon-baryon, and baryon-antibaryon channels. These include those giving rise to final states involving a heavy quark Q=c,b and antiquark Q¯′=c¯,b¯, namely, DD¯∗, D∗D¯∗, D∗B∗, B¯B∗, B¯∗B∗, ΣcD¯∗, ΣcB∗, ΣbD¯∗, ΣbB∗, ΣcΣ¯c, ΣcΛ¯c, ΣcΛ¯b, ΣbΣ¯b, ΣbΛ¯b, and ΣbΛ¯c, as well as corresponding S-wave states giving rise to QQ′ or Q¯Q¯′.