Your problem seems to be a matter of terminology. A PSK is a pocket survival kit. It is designed to be carried in the pocket so that you have it on you at all times. What you are talking about is a maxi kit A larger more extensive supply of gear. The difference you very well may be come seperated from your other gear but a pocket kit carries the bare minimum but is always with you.
Here are some definitions that may help clarify the difference in kits by size.
Micro: About the size of an old fashion pocket watch or smaller. These are usually job specific. Fire, water, fishing, ETC. The design is for these kits to be scattered around your person or gear to be combined to form a survival kit. The ultra small [micro] size makes for compact storage.
Mini: The size is to fit conveniently in a pocket. This should be a daily carry item. The standard is usually based on the Altoid tin. This is the true stand-alone survival kit. These kits try to meet the minimum needs in most situations. This can be made up of several micro kits. Also called PSK's or Pocket Survival Kits.
Maxi: The next step up in size and level of convenience. Usually from the size of a large paperback book to a hard bound one. This is where shelter material is starting to be added. You step up to this when you are planing to leave the beaten path.
Pack: This is the size of a butt or daypack. This is where you start adding food for several days. Such as a 72 hour kit. Usually combined with full camping gear. Carry this for short side trips or even if just going over there. If you go out of sight of the main camp you may need it.
Large: This is your camping gear and supplies for and extended trip out and beyond.
BOB: The whole enchilada. This is can be everything up to and may include the kitchen sink. This is the get out of town or get back home kit. Usually transported by vehicle but portions are person or persons portable. Usually a large backpack or duffel. Although it can range up to a packed trailer, fully stocked pop up travel trailer or even a RV.
_________________________
When in danger or in doubt
run in circles scream and shout
RAH
And always remember TANSTAAFL