答案选A。这是省略主语而用一个特殊不定式短语（通常用主动式）代替或简化定语从句，即：on which to base= on which he would base，which指代sufficient grounds。1984版高中英语第二册第14课“礼物（The Gifts）”中就有类似的一个表达：

Tomorrow would be Christmas Day, and she had only $1.87 with which to buy Jim, her husband, a present. 明天就是圣诞节了，她只有1美元87美分给她丈夫吉姆买礼物。

句中的with which to buy ...= with which she could buy...。