We present a novel surface acoustic wave sensor, incorporating the advantages of multi-frequency and multi-mode operation in a single acoustic device structure. SAW sensors are commonly based on the change of the effective elastic constants or the mass loading of the device due to a different sensor environment. Usually, single acoustic modes at a fixed frequency are employed allowing for the detection of a certain chemical species, depending on the coating of the wave's propagation path. Analyzing multiple acoustic modes or multiple excitation frequencies that are each reacting differently on a particular load, allows for the multi-parameter analysis of gases and liquids. We present a sensor system that is based on floating electrode unidirectional transducers (FEUDTs) allowing for the excitation of a set of 48 equally spaced frequencies and at least two acoustic modes (depending on the material system) in a single transducer structure. FEUDTs allow for the efficient excitation of acoustic waves at GHz frequencies without the use of sophisticated nanofabrication techniques. Higher frequencies, on the other hand, are advantageous for the sensitivity of the device. We tested the basic operation of our sensor system by applying it to humidity sensing without a sensitive layer.