Logistic Regression with Household Fixed Effects, SPSS

I have cross-sectional data on households and individuals for several countries.

I am interested in the marginal effect of a particular dichotomous individual variable $D_i$ (dummy denoting whether individual $i$ has some condition or not) on an individual outcome $Y_i$ (dummy denoting success).

Hence, I estimated the logistic regression

$\text{Pr}(Y_i=1)=\text{logit}^{-1}(\beta \boldsymbol{X}_i+\gamma D_i)$

where $\boldsymbol{X}_i$ is a vector of individual, household, and community control variables, e.g., age, age squared, gender, residential location, etc.

Now I wish to account for potential endogeneity of certain control variables on $D_i$ and $Y_i$ (i.e., some $x_i$ in $\boldsymbol{X}_i$ simultaneously affecting the likelihood of an individual experiencing condition $D$ and their outcome $Y_i$), by adopting a household fixed-effects approach.

A previous paper I am following simply re-estimated the regression on a subsample of individuals living in households where at least one individual had the condition and one did not, replacing all household and community variables with dummy variables for each household minus one.

However, reading suggests I cannot simply estimate the revised logistic regression

$\text{Pr}(Y_i=1)=\text{logit}^{-1}(\beta' \boldsymbol{X'}_i+\gamma' D_i+\sum\delta_j {H_j}_i)$

where ${H_j}_i$ is a dummy denoting whether individual $i$ is resident in household $j$ or not, because serious coefficient bias will arise given the small number of observations per household (similar to having a small number of $T$ in a panel fixed-effects modeL).

Instead, it has been advised to use a conditional logit fixed effects estimator.

(1) Is this possible in SPSS, and if so, how?

(2) Will this allow computation of the marginal effect of $D_i$?

(3) If not, is it preferable to adopt instead a linear probability model?