@Xwl522How did you get this value? Depending on how it was obtained, it may actually be a different data type and that is just the first byte. Try editing the value as dword instead of byte (click the value, hit goto address, then hit it again and select edit - this type it should ask you which data type you want to edit it as).
However, if that byte does reflect the value in the game and editing is as dword doesn't work, then it is indeed of byte type. If this is the case, then you simply cannot exceed 255. Just like you can't edit a dword value past the integer limit.
Instead of asking how, you should be asking why. If a value is of byte type, that means the game will never need it to be greater than 255. So why do you need it to be? For example, currency will never be stored as byte (unless that type of currency happens to be extremely rare, and in that case, editing it to 255 should be more than enough of it).
So if it is of byte type, then no, you can't make the value greater than 255 - but you shouldn't need to.