If your dulcimer is a standard size with a scale length of 25-29", it's unlikely you could tune a thin string way up to the "a" above the usual high d. Once you use a .007 or thinner string, and tune it up to such a high note on the standard size scale, that very thin string will almost certainly break under the tension. There's only so far you can go with the method of using a thinner string to tune higher and a thicker string to tune lower... going too far will mean a string so fat it will be unplayable and thuddy, or a string so thin it will simply break before it reaches the extreme high note. When you've reached those string gauge extreme limits either way (too low or too high), the next step is to switch to an instrument with a longer scale or a shorter scale, so that you CAN tune to those notes without having to use impossibly heavy or thin strings.
Dusty brings up some good thoughts in his post. And I too am curious about your goal in tuning this way. :)
Those irritated by grain of sand best avoid beach.
-Strumelia proverb c.1990