# 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?