I would not try to do this with Express MaxDiff. Rather, I'd continue with the Sparse MaxDiff approach--if respondents cannot see each item 1x, then you can do the Sparse MaxDiff approach with each respondent seeing each item fewer than 1x on average.
For example, imagine you have 200 items and you plan to show 5 items per MaxDiff set, for 20 total sets. That means under Sparse MaxDiff each respondent will see half the items. Make sure to click the button in the Design tab (under Show Advanced Settings that says "Allow Individual Designs Lacking Connectivity").
However, I would prefer not to use HB for analysis when each respondent hasn't seen each item. I would think you would be limited to pooled analysis, such as aggregate logit for the sample.
And, given the sparse nature of your design, I would do some pre-planning to evaluate how many times each item would be displayed across respondents. My personal preference is that for large sparse designs like this I want each item to appear at least 1000 times across the sample. So, since it takes two respondents to see each item once, it means you'll want to have at least n=2000.
If the main purpose of your research is to identify the top winning few items out of the 200, then the Bandit MaxDiff approach as supported by interviewing in our Lighthouse Studio platform is 3x to 5x more efficient than sparse MaxDiff. In other words, rather than using 2000 sparse MaxDiff respondents, you could obtain equally precise results (in terms of identifying the top few items) using from 400 to 667 respondents.