Some Russian researchers investigating Siberian Ginseng observed that these deep immune tonics seem to generally aid the body in dealing with stress and coined the term "adaptogen" for them.
(see "adaptogens" in "herbology" under "modalities" for a discussion of these herbs as adaptogens: a paper similar but slightly different from this one)
Deep immune tonics/adaptogens need to be used over a relatively long period of time (six weeks, for example).
Again, as with most herbs "the formula is the thing": they work better, synergistically, in combination.

Asian Ginseng    Panax ginseng

deep immune tonic, adaptogen

Asian Ginseng is a "hot" remedy (best used for "cold" conditions)

North American Ginseng    Panax quinquifolium

deep immune tonic, adaptogen

North American Ginseng is considered a "cold" remedy (best used for "hot" conditions)

Siberian Genseng    Eleutherococcus senticosus

deep immune tonic, adaptogen, circulatory tonic, surface immune stimulant, antineoplastic

Eleuthero has most of the properties of its cousin, Ginseng, but is neither "hot" nor "cold" and is therefore of more general use.
It is a useful part of almost any immune support formulation and is helpful in chemotherapy both in reducing side effects (as an adaptogen) and in enhancing the therapeutic effects of the chemotherapy.

Astragalus    Astragalus membranaceus

deep immune tonic, adaptogen, surface immune stimulant, antineoplastic

synergistic with Siberian Ginseng, and with Echinacea.
It is helpful in chemotherapy both in reducing side effects (as an adaptogen) and in enhancing the therapeutic effects of the chemotherapy.

Reishi mushrooms    Ganoderma lucidum

deep immune tonic, adaptogen, surface immune stimulant, antineoplastic, antiviral

may be used in small doses as a "potentizer"
should be used for 4 to 6 weeks (and then only repeated after a "holiday" of 4 to 6 weeks).
Can be used in severe immune depletion such as AIDS and cancer.
Particularly useful in lymphoma with, for instance, cleavers and phytolacca.
It is helpful in chemotherapy both in reducing side effects (as an adaptogen) and in enhancing the therapeutic effects of the chemotherapy.

see also:Reishi.com

Other adaptogens/deep immune tonics include:

Shataki mushroom
Maitaki mushroom (the "D fraction")
Spiknard
False Sarsaparilla

for Taheebo/Pau d'Arco see
        surface immune stimulants

A formulation might include:

Siberian Ginseng         10 drops
Reishi                              5 drops
Astragalus                     10 drops

three times a day, in water, before meals, for 4 to 6 weeks