Henry is usually happy to modify his designs to accommodate personal taste or necessity (enabling a bag to perform a particular function). The added expense is relative to the amount of extra work.
Copying an existing bag of yours might be possible if you can provide him with the bag itself to take a pattern from. This is likely to cost MUCH more than the original but will not necessarily be an improvement.
Henry can sometimes make a bag based on itemised specifications (detailed measurements/drawings etc.) Aside from the expense of this route, there can sometimes be unforeseen consequences to certain design decisions. Henry’s long experience at improvising can usually spot these pitfalls, but be prepared to compromise!