Mode-division　multiplexing　(MDM)　greatly　enhances　the　capacity　of　on-chip　photonic　interconnects,　yet　traditional　MDM　techniques　struggle　with　direct　access　to　specific　lower-order　modes　within　multimode　bus　waveguides,　limiting　scalability　and　flexibility.　In　this　paper,　we　introduce　a　compact　and　flexible　MDM　architecture　featuring　an　engine　that　combines　a　grating-engineered　backward　mode　converter　(BMC)　with　a　bidirectional　asymmetric　directional　coupler　(Bi-ADC).　The　BMC　is　precisely　engineered　to　leverage　the　modal　properties　of　the　multimode　bus　waveguide,　enabling　efficient　switching　between　two　designated　modes　while　minimizing　crosstalk　with　other　modes.　The　Bi-ADC　operates　analogously　to　a　2　x　2　coupler　and　integrates　a　single-mode　access　waveguide　with　the　bus　waveguide,　allowing　for　independent　routing　of　two　modes　through　the　access　waveguide＇s　ports.　This　approach　provides　a　more　compact　design　compared　to　conventional　MDM　techniques　and　facilitates　the　insertion　of　lower-order　modes　at　arbitrary　positions　along　the　bus　waveguide.　Furthermore,　this　architecture　can　be　combined　with　an　optical　switch　to　develop　a　bidirectional,　dual-mode　switchable　add-drop　mode　multiplexer.　To　demonstrate　its　feasibility,　we　design　two　BMC-based　engines　for　TE0-TE1　and　TE0-TE2　mode　conversions　and　assess　their　performance　numerically　as　4-mode/5-mode　demultiplexers.　Experimental　results　showcase　a　4-channel　mode　demultiplexer　(TE0,　TE1,　TE2,　and　TM0)　based　on　the　TE0-TE1　engine,　achieving　insertion　losses　(ILs)　of　2.4　dB,　0.3　dB,　1.28　dB,　and　0.75　dB　at　a　wavelength　of　1550　nm.　The　modal　crosstalk　is　below　-17.5　dB　for　all　channels,　with　an　IL＜3　dB　bandwidth　exceeding　100　nm.