As the inventory of interstellar molecules continues to grow, the gulf between small species, whose individual rotational lines can be observed with radio telescopes, and large ones, such as polycyclic aromatic hydrocarbons best studied in bulk via infrared and optical observations, is slowly being bridged. Understanding the connection between these two molecular reservoirs is critical to understanding the interstellar carbon cycle, but will require pushing the boundaries of how far we can probe molecular complexity while still retaining observational specificity. Towards this end, we present a method for detecting and characterizing new molecular species in single-dish observations towards sources with sparse line spectra. We have applied this method to data from the ongoing GOTHAM (GBT Observations of TMC-1: Hunting Aromatic Molecules) Green Bank Telescope large programme, discovering six new interstellar species. Here we highlight the detection of HC₁₁N, the largest cyanopolyyne in the interstellar medium.