You (and all of us) are looking for the best model to fit the data. That is the model that describes the highest percentage of variation within the data (highest R or adjusted R). At the same time you would want to include the relevant variables (predictors) that significantly affect the dependent variable or the outcome without going through issues like collinearity or confounding.

If you're not sure which predictors are most important without interferring with others, I'd do univariate (unadjusted) regressions then do stepwise regression.

If the associations between the independent variables are strong, we have multicollinearity. This can be a serious problem in regression analysis as it can artificially create a high R square; very large regression coefficients in magnitude; very large prediction variance; incorrect signs for the regression coefficients ... etc. Stepwise regression does not detect multicollinearity, and it has many problems.

Do you have access to SAS? Which software are you using?

For the purpose of knowing the best regression model you should

make sure there are no data problems (Normal distribution, no outlier or contamination)و  in the case of either of them, the Robust regression analysis is used, there are several benchmarks to compare as(MSE, R2,p-value).

best regards

To address the main question, it's up to you if you want to build one model with a variety of variables, or multiple models with only similar variables.  It depends upon your goal.

But in either case, as the other answers point out, you may not be able to include all the variables in the model, and you must use care in constructing the model.

There are several methods used to identify the best model for your regression analysis. You may try to do multiple model and see which one has the best goodness of fit and best explains the variability of your outcome with the highest proportion. Regards