Washing for Hamotzi More Than Three Times on Shabbos

Thank you for your question.

There is no issue with washing for bread and making Hamotzi more than three times on Shabbos. However, at each meal, one should make Hamotzi on lechem mishneh (two loaves), as brought in the Rema;

שולחן ערוך, אורח חיים, הלכות שבת, סימן רצא, סעיף ד
ואם סועד הרבה פעמים בשבת צריך לכל סעודה ב' ככרות (אבודרהם ומיימוני).

Shulchan Aruch, Orach Chaim, Laws of Shabbos, 291:4
If one eats several meals on Shabbos, one must have two loaves of bread for each meal. (Abudraham and Maimonides)

Wishing you all the best.