Motivated by recent experiments on BaCu Si2 O6, we investigate magnetic excitations and quantum phase transitions, driven either by pressure or magnetic field, of layered dimer magnets with interlayer frustration. We consider two scenarios, (A) a lattice with one dimer per unit cell and perfect interlayer frustration, and (B) an enlarged unit cell with inequivalent layers, with and without perfect frustration. In all situations, the critical behavior at asymptotically low temperatures is three-dimensional, but the corresponding crossover scale may be tiny. Magnetic ordering in case (B) can be discussed in terms of two condensates; remarkably, perfect frustration renders the proximity effect ineffective. Then, the ordering transition will be generically split, with clear signatures in measurable properties. Using a generalized bond-operator method, we calculate the low-temperature magnetic properties in the paramagnetic and antiferromagnetic phases. Based on the available experimental data on BaCu Si2 O6, we propose that scenario (B) with inequivalent layers and imperfect frustration is realized in this material, likely with an additional modulation of the interlayer coupling along the c axis.