An extended comment.
If I read your question correctly, memory appears to limit your calculations rather than the number of computing kernels.
Following this line of thought, it would help responders to know if your problem comes from processing large data sets, complexity of calculation, calculations that just need lots of memory, or some combination of these.
Some other information would also help, like your computing environment's specifications: CPU, RAM, HD, OS,
Some things to try immediately:
Reboot your laptop.
To the degree possible don't open any applications other than Mathematica.
Run your calculations and see if you still get the same errors.
IF you still have the problem, can you identify and isolate the specific code or function that generates the out-of-memory errors? This would enable people on the site to suggest specific alternatives that may work around the problem (adding various kinds of constraints, options, or specifying a domain for lots of functions can often solve these kinds of issues).
Beyond this, if memory rather than CPU really does limit you, I wonder if you could allocate more virtual memory or even set up remote virtual memory.
Certainly cumbersome, probably impractical, and VERY SLOW, but it might provide you a way to do the calculations without investing in additional Mathematica licenses.