  We present a method that uses radio-frequency pulses to cancel the quadrupole
shift in optical clock transitions. Quadrupole shifts are an inherent
inhomogeneous broadening mechanism in trapped ion crystals, limiting current
optical ion clocks to work with a single probe ion. Cancelling this shift at
each interrogation cycle of the ion frequency allows the use of $N>1$ ions in
clocks, thus reducing the uncertainty in the clock frequency by $\sqrt{N}$
according to the standard quantum limit. Our sequence relies on the tensorial
nature of the quadrupole shift, and thus also cancels other tensorial shifts,
such as the tensor ac stark shift. We experimentally demonstrate our sequence
on three and seven $^{88}\mathrm{Sr}^{+}$ ions trapped in a linear Paul trap,
using correlation spectroscopy. We show a reduction of the quadrupole shift
difference between ions to $\approx20$ mHz's level where other shifts, such as
the relativistic 2$^{\mathrm{nd}}$ order Doppler shift, are expected to limit
our spectral resolution. In addition, we show that using radio-frequency
dynamic decoupling we can also cancel the effect of 1$^{\mathrm{st}}$ order
Zeeman shifts.
