There are several possible options depending on what data are available and whether you have the opportunity to follow some or all of the cohort in the cross sectional study. If you can link data that had been previously collected to the cross sectional study you can look at the influence of various measures on the outcomes you have the in the CS study. For example, is iron deficiency related to restless leg syndrome. If you have information on the outcome, restless leg, you could see if people with repeated reports of iron deficiency have a higher risk of the condition. Also, it is possible to follow the cohort to see if conditions develop. An example would be the cross sectional study examined Ig levels and prior history of health effects. You could follow the whole or a sample of the cohort and look at the frequency prospectively of infectious diseases. This could yield valuable information. You could choose the new population based on some criterial of interest. What we call the design is less important than the protocol and the questions you want to address.
I hope this is helpful. No doubt many might not agree.
Thank you very much for sharing your concerns. If you carry out a cross-sectional study and later on wish to perform a secondary analysis, the design/type of secondary study will entirely depend on your new objectives. But usually, secondary analysis of cross-sectional data will yield observational studies (which may be descriptive, analytic). You may also generate an article review of your primary cross-sectional study.
You may carry out a meta-analysis or systematic review of studies with similar objectives as your cross-sectional study (and even cite your study) and they may all be of different study designs. Nonetheless, the meta-analysis/systematic review will be an entirely different study and in a strict sense will not be considered a secondary analysis.