Does tire pressure drastically affect crosswind stability?

It's an 04 F-53 with the long wheel base and very short rear overhang. I haven't weighed it but, I'm sure it is well under the ratings for the chassis and the tires, so, I'm not concerned about underinflation. It has never wagged tne tail, so, I doubt that a track bar whould help much. I guess I'll just start by taking the pressure up twenty pounds and then go from there. I'll let you know the results. Thanx for the suggestions and experiences.