If these base cards are just titles then why have the data rows contained within a card at all? This seems like the perfect case of running a simple data table that the user can filter with a free text search to target the types and content of the rows that will be the of the most interest to them.
Now if this base card idea was done for performance reasons then it kind of makes since as long as the card carries a count of how may rows will be displayed when opened. This will help inform the user of the impact of their choice of opening a card.
In essence though what it seems to be is the same issue that most retailers have already tackled with a left hand filter set married with a free text search and then just displaying the results as either table line items or cards. Either way your starting idea seems to create more surprises for the users rather than provide them with information to guide them to the work they need to do.