soften (one's or someone's) stance (on something)
1. To become less severe, strict, or inflexible in one's position or beliefs (regarding something). Our dad always said he would never let us have our own phones, but he softened his stance when my sister and I started high school. The senator has indicated that she may be softening her stance on the issue of tax reform.
2. To cause someone else to become less severe, strict, or inflexible in their position or beliefs (regarding something). I've been trying to soften the boss's stance on giving paid parental leave to all new employees. The government was originally adamant in their position on the controversial issue, but the continual protests around the country seem to be softening their stance.
soften one's stance (on someone or something)
Fig. to reduce the severity of one's position regarding someone or something. If he would soften his stance on the matter, I could easily become more cooperative.