  We extend the GENEVA Monte Carlo framework using the transverse momentum of a
colour-singlet system as the resolution variable. This allows us to use
next-to-next-to-next-to leading logarithm (N$^3$LL) resummation via the \radish
formalism to obtain precise predictions for any colour-singlet production
process at the fully exclusive level. Thanks to the implementation of two
different resolution variables within the GENEVA framework, we are able to
assess the impact of such a choice on differential observables for the first
time. As a first application we present predictions for Drell-Yan lepton pair
production at next-to-next-to-leading order (NNLO) in QCD interfaced to a
parton shower simulation that includes additional all-order radiative
corrections. We provide fully showered and hadronised events using PYTHIA8,
while retaining the NNLO QCD accuracy for observables which are inclusive over
the additional radiation. We also show that it is possible to obtain a
numerically good agreement between showered GENEVA predictions and the N$^3$LL
resummation for the transverse momentum spectrum by choosing a more local
recoil scheme. We compare our final predictions to LHC data at 13 TeV, finding
good agreement across several distributions.
