Q. Is there a book or best resource through PHS you recommend for transplanting as to when it should be done?
Transplanting techniques and timing vary significantly depending on where the plant is growing and the type of plant, e.g., trees, shrubs, perennials, annuals or houseplants -- and whether they are in the ground, in pots, are seedlings or cuttings or mature plants.
For growing outdoors, I recommend Liz Ball's book Month-by-Month Gardening in Pennsylvania. This book is in the PHS library and, as a PHS member, you may borrow this book. Call 215-988-8772 to learn how.
For indoor plants, the best information on when and how to transplant will be in books that cover the indvidual families or genus. Plants that do well when pot bound may require more frequent watering. Some plants require division when transplanting. And transplanting can be part of a broader plant care regime. You will need to consult different books for indoor plants. I reviewed some of the standard books we use at the Ask-A-Gardener desk and found some of the best reference books we use, such as the A-Z Encyclopedia, did not cover transplanting. Another one, Indoor Plants by Halina Heitz did a good job integrating plant care with transplanting advice, but did not cover all houseplants.