Variable order in InterpolatingFunction

I’m attempting to deal with a interpolating a function $f[x,t]$ on an unevenly spaced grid of $n$ points. My x-variable is continuous, so there’s no difficulty in fitting a cubic spline to it with InterpolationOrder$to$3 for $f[x,1]$, but because I can’t violate causality and fit using future data, I need to ensure that InterpolationOrder$to$0 for $f[1,t]$.

Is it possible to do this nativley in any way using the Interpolate command? Or would the best way be to set up $n$ different univariate $x$-Interpolations at each of my measured $t=t_i$ coordinates and connect them with some messy If statement?