You can load the 6.5X55 to 'modern pressures', ie 60-62,000 psi. Whether it's wise and safe to do so even in a modern strong action is debatable (to understate the matter). I handload 6.5X55 using Norma and Lapua brass for long-distance F-Class, and frankly wouldn't ever consider loading it to those pressures, or anything near!
Actually, because of the considerable degree of body taper, the 6.5X55 only offers a modest amount of extra capacity over modern designs based on the 308 Win case or the even less tapered Creedmoor (based on the Hornady/Thompson Center .30TC case). Lapua 6.5X55 cases from my match rifle chamber hold 58.1gn water. That compares to 53.7gn with Hornady 6.5 Creedmoor fireformed brass and around 55gn from Lapua 260 Rem. That's an 8.2% increase 6.5X55 vs 6.5CM. The standard rule of thumb is that all other things being equal, an x% case capacity change gives 0.25x% MV change, ie +2.05% here. So, if you have a Creedmoor load giving 2,800 fps from a 140gn bullet you can expect an additional 57 fps.
However that applies only if all other things are the same - barrel length; bullet; chamber pressure. In this pair, you are comparing a 51/55,000 psi design to a 62,000 psi one and things are definitely not equal.