This work considers nonlinear phenomena in one-dimensional piecewise linear maps with two discontinuities. These maps are written in a standart form and are studied in the stable regime with all slopes between zero and one. Based on previous results from maps with one discontinuity this work does a priliminary analysis and outlines the new bifurcation structures found in the maps with two discontinuities. Several different parameter configurations are considered and investigation is primarily focused on orbits located on all three partitions. The underlying bifurcation types causing the found structures are investigated as well.