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On-chip mode-division multiplexing (MDM) has been emerging as a promising technology to further enhance the link capacity and bandwidth of data communications with multiple mode channels. Both mode converters and mode exchangers are indispensable fundamental components for flexible mode operations. While several configurations have been developed previously, it is still very challenging to efficiently manipulate arbitrary high-order modes in a versatile way to reduce the R&D and prototyping costs. Here we initiate a breakthrough with a simple yet universal generic mode operator building block concept utilizing metasurface structures. The programmable arbitrary high-order mode operators can realize mode conversion and exchange simultaneously with competitive and uniform performance, high stability and compact footprints, offering a quintessential step change for on-chip multimode optical interconnections.