Baade-Wesselink-type (BW) techniques enable geometric distance measurements of Cepheid variable stars in the Galaxy and the Magellanic clouds. The leading uncertainties involved concern projection factors required to translate observed radial velocities (RVs) to pulsational velocities and recently discovered modulated variability. We carried out an unprecedented observational campaign involving long-baseline interferometry (VLTI/PIONIER) and spectroscopy (Euler/Coralie) to search for modulated variability in the long-period (P~35.5d) Cepheid {ell} Carinae. We determine highly precise angular diameters from squared visibilities and investigate possible differences between two consecutive maximal diameters, {Delta}max{Theta}. We characterize the modulated variability along the line of sight using 360 high-precision RVs. Here we report tentative evidence for modulated angular variability and confirm cycle-to-cycle differences of {ell} Carinae's RV variability. Two successive maxima yield {Delta}max{Theta}=13.1+/-0.7(stat.){mu}as for uniform disc models and 22.5+/-1.4(stat.){mu}as (4 percent of the total angular variation) for limb-darkened models. By comparing new RVs with 2014 RVs, we show modulation to vary in strength. Barring confirmation, our results suggest the optical continuum (traced by interferometry) to be differently affected by modulation than gas motions (traced by spectroscopy). This implies a previously unknown time dependence of projection factors, which can vary by 5 percent between consecutive cycles of expansion and contraction. Additional interferometric data are required to confirm modulated angular diameter variations. By understanding the origin of modulated variability and monitoring its long-term behaviour, we aim to improve the accuracy of BW distances and further the understanding of stellar pulsations.