Looking for the Concept About All In One Curve Fitting
You can always augment the matrices to do so.

Let's assume the first model is given by:

$$ {y}_{1} = {H}_{1} * {\theta}_{1} $$

The second model is given by:

$$ {y}_{2} = {H}_{2} * {\theta}_{2} $$

The third model is given by:

$$ {y}_{3} = {H}_{3} * {\theta}_{3} $$

If we assume the number of parameters of the model are the same, namely $ {\theta}_{1}, {\theta}_{2}, {\theta}_{3} \in {\mathbb{R}}^{d} $ and $ {y}_{i} \in {\mathbb{R}}^{{n}_{i}} $ by the following augmentation:

$$ y = H \theta $$

Where $ y = {\left[ {{y}_{1}}^{T}, {{y}_{2}}^{T}, {{y}_{3}}^{T} \right]}^{T} $, $ H = {\left[ {{H}_{1}}^{T} \mid {{H}_{2}}^{T} \mid {{H}_{3}}^{T} \right]}^{T} $ and $ y = {\left[ {{\theta}_{1}}^{T}, {{\theta}_{2}}^{T}, {{\theta}_{3}}^{T} \right]}^{T} $ you can get:

$$ \hat{\theta} = {\left( {H}^{T} H \right)}^{-1} {H}^{T} y $$

Extracting the the corresponding parameters is easy.

If the parameters vectors are not the same dimension, you can use zeros to make everything work.