You have already read those Oppenheim's Signals & Systems, and Discrete-Time Signal Processing books.
I'm not sure what you mean by foundations but in some sense these two are also the foundations on signal processing. In other words, there are no (popular & successful) graduate level DSP books that discuss at an advanced level the same topics that are covered on them.
However the following books (or subjects) will enhance your understanding, or broaden your appreciation of the subject.
First of all, the very first graduate level course on DSP, Communications, and Control is called Linear System Theory which brings together all the undergraduate mathematical stuff from a new, advanced, deeper, and foundational point of view of the Hilbert (linear vector) Spaces, Linear Mappings, and Matrix theory. It does not have a definite book but a bunch of books on Linear Algebra & Matrices, Measure Theory, and Diferential Equations were used. Note that there's a control theory oriented bunch of Linear System Theory books (Desoer's crew) that I do not recommend for DSP, unless you will be designing control systems on the field. Signal processing does not make much use of state-space approach, unless it's absolutely necessary.
Then the second refresher/deepener is on Probability, Statistics and Random Processes. Fortunately it has two very strongly recomended books though:
- Statistical Digital Signal Procesing _ Monson HAYES
- Discrete RaNdom Signals and Statistical Signal Processing _ THERRIEN
The first book is a must read, the second one is following the style of Oppenheim series but is harder to follow, and less practical than the first.
Then the following books / subjects will be awating you :
- Adaptive Filter Theory _ HAYKIN
- Multiresolution Signal Decomposition _ AKANSU
- Multirate Digital Signal Processing _ RABINER
- Estimation & Detection Theory _ KAY
- Pattern Classification _ DUDA
- Theory and Applications of Digital Signal Processing _ RABINER & GOLD
Then the following applications will make your day :
Speech and Hearing for Communication - FLETCHER
Digital Processing of Speech _ Rabiner
Speech and Audio Signal Processing _ GOLD
Discrete-Time Processing of Speech _ PROAKIS
Advances in Speech Coding _ GERSHO
Two-Dimensional Signal and Image Processing _ LIM
Digital Image Processing _ GONZALES
Fundamentals of Image Processing _ JAIN
Introduction to Data compression _ SAYOOD
Of course the list is by no means complete...