"Adjusting for a covariate" can mean many things. I suspect that additive corrections might be most common, but that doesn't mean that limiting yourself to them is best. If an interaction is important and isn't included, you are likely to get biased results, lower power, and less of an ability to extend results to a population that has different prevalences of the values of the interacting predictors that are associated with outcome.
A good overall strategy in regression modeling, particularly with survival modeling, is thus to work with as complex a model as is reasonable. Frank Harrell's class notes and book, particularly Chapter 4, present useful introductions to multivariable regression modeling strategies.
The problem you face is the relatively small number of cases relative to the number of predictors. Survival modeling is at risk of overfitting if you evaluate more than 1 unpenalized predictor per 10-20 events, with each level of a categorical predictor beyond the first and each interaction term counting as a separate predictor. So unless you do some type of penalization, you are limited to about 6 predictors including interactions.
If you have one binary predictor of primary interest and 3 categorical predictors as covariates, you might be able to get away with each of those as additive terms plus interactions of the primary predictor with each of the covariates separately (total of 7 predictors including interactions). It would be wise to evaluate that model for overfitting with the "optimism bootstrap" explained in Chapter 5 of Harrell and implemented in the validate() function of his rms package in R.
If some of your categorical predictors have more than 2 levels, you need to examine interactions among the covariates not of primary interest, or you have additional covariates to control for, then adding the corresponding extra terms is likely to overfit. You can cut down on the effective number of covariates by combining them usefully first without regard to outcome (Chapter 4 of Harrell) or by using ridge regression to penalize the covariates that aren't of primary interest. See for example the discussion of penalization by Pavlou et al and the comparison by Chen et al of different ways to deal with "too many covariates and too few cases." Penalization reduces the magnitudes of covariates, minimizing overfitting while allowing evaluation of more covariates than otherwise would be possible.
Finally, note that this type of control for covariates can fail if there is confounding (a "treatment," your primary predictor of interest here, and outcome having a common cause), selection bias, or measurement bias. Hernán and Robins discuss those types of complications and ways to deal with them.
