  We investigate generalized Einstein-Aether theories that are compatible with
the Planck Cosmic Microwave Background (CMB) temperature anisotropy,
polarisation, and lensing data. For a given dark energy equation of state,
$w_{\rm de}$, we formulate a designer approach and we investigate their impact
on the CMB temperature anisotropy and matter power spectra. We use the Equation
of State approach to parametrize the perturbations and find that this approach
is particularly useful in identifying the most suitable and numerically
efficient parameters to explore in a Markov chain Monte Carlo (MCMC) analysis.
We find the data constrains models with $w_{\rm de} = -1$ to be compatible with
$\Lambda$CDM. For $w_{\rm de} \not= -1$ models, which avoid the gravitational
waves constraint through the entropy perturbation, we constrain $w_{\rm de}$ to
be $w_{\rm de } = -1.06^{+0.08}_{-0.03}$ (CMB) and $w_{\rm de }
=-1.04^{+0.05}_{-0.02}$ (CMB+Lensing) at $68\%$C.L., and find that these models
can be different from $\Lambda$CDM and still be compatible with the data. We
also find that these models can ameliorate some anomalies in $\Lambda$CDM when
confronted with data, such as the low-$\ell$ and high-$k$ power in the CMB
temperature anisotropy and matter power spectra respectively, but not
simultaneously. We also investigate the anomalous lensing amplitude, quantified
by $A_{\rm lens}$, and find that that for $w_{\rm de} = -1$ models, $A_{\rm
lens} = 1.15^{+0.07}_{-0.08}$ (CMB) and $A_{\rm lens} = 1.12\pm0.05$
(CMB+Lensing) at $68\%$C.L. $\sim$ 2$\sigma$ larger than expected, similar to
previous analyses of $\Lambda$CDM.
