I understand you are looking for a sub-national geography variable that is roughly comparable between samples, so that your geographic fixed effect is as similar as possible for all of the countries in your analysis. We received your email on the same topic, which also mentioned that you are considering using DOMAIN or STRATA as your geographic fixed effect variable.
Inherently, the way that sub-national geographic units are defined are specific to each country, and are not typically perfectly comparable between countries. While IPUMS User Support does not provide analytical guidance, I would suggest considering which characteristics you want to hold constant, as this may guide the level of geography you choose, and whether you allow it to vary by country.
Standard region seems suitable to me for sub-national geographic fixed effects. When you employ geographic fixed effects, you then only compare observations within the same geographic area. It does not seem inappropriate to me to compare observations within regions that are defined for each specific country. IPUMS DHS does not currently provide the standard region (V024) variable. However, we do provide sample-specific geography variables, as well as spatially harmonized country-specific geography variables. You can read about the geography variables we offer on this page. The IPUMS DHS variable GEOLEV2 might be appropriate for your purposes. GEOLEV2 provides consistent second-level administrative units for each country included across sample years to facilitate comparisons over time. This variable is available for many, but not all, DHS samples.
You’re correct that DOMAIN would not be appropriate for sub-national geographic fixed effects. As you noted in your email, DOMAIN identifies different levels of geography by sample depending on how the weights were formulated (e.g., you may be using urban/rural controls, region fixed effects, or no fixed effects, depending on the sample, which is not what you intend). And DOMAIN equals zero for all respondents in samples that are self-weighted to be nationally representative (but not representative at smaller geographic levels).
STRATA would be more appropriate than DOMAIN as a geographic fixed effect. The Guide to DHS Statistics provides useful information on what strata are, which may help you determine whether using this variable as a geographic fixed effect is suitable for your research. From page 1.33 of the guide:
DHS sample designs are usually two-stage probability samples drawn from an existing sample frame, generally the most recent census frame. A probability sample is defined as one in which the units are selected randomly with known and nonzero probabilities. A sampling frame is a complete list of all sampling units that entirely covers the target population. Stratification is the process by which the sampling frame is divided into subgroups or strata that are as homogeneous as possible using certain criteria. Within each stratum, the sample is designed and selected independently. The principal objective of stratification is to reduce sampling errors. In a stratified sample, the sampling errors depend on the population variance existing within the strata but not between the strata. Typically, DHS samples are stratified by geographic region and by urban/rural areas within each region.
Since DHS samples are typically stratified by geographic region and by urban/rural areas within each region, one stratum will usually correspond roughly to an urban or rural area of a single geographic region.
You may also want to review the literature in your field to determine what other researchers have done to include geographic fixed effects when pooling data from multiple countries.