Experimental and theoretical investigations on itinerant ferromagnetic systems under pressure have shown that ferromagnetic quantum criticality is avoided either by a change of the transition order, becoming of the first order at a tricritical point, or by the appearance of modulated magnetic phases. In the first case, the application of a magnetic field reveals a wing-structure phase diagram as seen in itinerant ferromagnets such as ZrZn2 and UGe2. In the second case, no tricritical wings have been observed so far. Here, we report on the discovery of wing-structure as well as the appearance of modulated magnetic phases in the temperature-pressure-magnetic field phase diagram of LaCrGe3. Our investigation of LaCrGe3 reveals a double-wing structure indicating strong similarities with ZrZn2 and UGe2. But, unlike these simpler systems, LaCrGe3 also shows modulated magnetic phases similar to CeRuPO. This finding provides an example of an additional possibility for the phase diagram of metallic quantum ferromagnets.