When optimizing parameters, how to increase or decrease the parameters participating in optimization without modifying the code

L is parametaer needing to be optimized. We do not care about other parameters. The actual fun is complex,but I simplified it to following fun.

fun=@(x1,x2,t,L) x1 .* x2 .* (L(1)+L(2)*t);

[L,resnorm] = lsqnonlin(@(L)fun(x1,x2,t,L)-y, [0 0])

If the optimization result is not good, I need to add an L(3),L(4)：

fun = x1 .* x2 .* (L(1)+L(2)*t+L(3)*t^2)

fun = x1 .* x2 .* (L(1)+L(2)*t+L(3)*t^2+L(4)*t^3)

And so on.

So I want to know how I can write code so that I can modify the optimized parameters without modifying the code of this fun. I know that many items of L may need to be written in advance in code, and then the optimized parameters can be selected. How to achieve it, I hope you can give me a solution or idea, I will be very grateful to everyone.