International audienceWe explore the possibilities for a next-generation electron-electric-dipole-moment experiment using ultracold heteronuclear diatomic molecules assembled from a combination of radium and another laser-coolable atom. In particular, we calculate their ground state structure and their sensitivity to parity- and time-reversal () violating physics arising from flavor-diagonal charge-parity () violation. Among these species, the largest -violating molecular interaction constants—associated for example with the electron electric dipole moment—are obtained for the combination of radium (Ra) and silver (Ag) atoms. A mechanism for explaining this finding is proposed. We go on to discuss the prospects for an electron EDM search us...