Let's proceed step by step and clarify the **Specified Physicochemical Properties** relevant for classifying these **bases**. Common and database-accessible quantitative properties for bases include:

- **pKa (of the conjugate acid):** Quantitative indicator of basic strength.
- **Basicity indices (e.g., pKb, proton affinity):** Quantitative measure of how readily the substance accepts a proton.
- **Number of Nitrogen Atoms (Potential basic sites):** Countable and often tabulated.
- **Steric bulk indices (e.g., cone angle, A-values):** Sometimes quoted.

For organic superbases, we generally find:
- **pKa (conjugate acid) higher than typical amines (commonly > 13, often in the 20–35 range).**
- **Sterically hindered or guanidine-type nitrogen environments.**

### Step 1: Collect Likely Relevant Quantitative Data

#### 1. **1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine**
- Common name: Likely an analog of a highly substituted diamine, perhaps a "proton sponge"-like bicyclic amidine.
- **Nitrogen count:** 2 (in the bicyclic system)
- **Approximate pKa (conjugate acid):** Estimated range 13–15 (similar to 1,8-bis(dimethylamino)naphthalene)
- Not a guanidine superbase.

#### 2. **2-tert-butyl-1,1,3,3-tetramethylguanidine**
- **Nitrogen count:** 3 (guanidine core)
- **Approximate pKa (conjugate acid):** ~13–15 (for guanidines, e.g., tetramethylguanidine pKa ≈ 13.6, tert-butyl substituted may be similar or slightly higher)
- **Steric bulk:** High, due to tert-butyl group.

#### 3. **N-[dimethylamino-ethylimino-[[tris(dimethylamino)-lambda5-phosphanylidene]amino]-lambda5-phosphanyl]-N-methylmethanamine**
- This is a phosphazene base (e.g., t-Bu-P4 type).
- **Number of nitrogen atoms:** 6–8 (from the numerous dimethylamino groups attached to phosphorus centers)
- **Approximate pKa (conjugate acid):** 25–42 (typical for phosphazene superbase family, e.g. P2-Et pKa ≈ 27.6, P4-tBu pKa > 40 in acetonitrile)
- **Basicity:** Among the strongest known neutral organic bases.

### Step 2: Define Categories for Grouping

Given the data, **pKa of the conjugate acid** is the best-well tabulated, quantitative criterion.

Let us attempt to make NO MORE THAN THREE groups, defined by:
- **Group A:** Moderately strong bases (pKa of conjugate acid 12–16)
- **Group B:** Superbases, non-phosphazene (pKa of conjugate acid 17–24)
- **Group C:** Phosphazene superbases (pKa of conjugate acid ≥25)

### Step 3: Assign Each Substance

#### **Group A: Moderately strong bases (pKa 12–16)**
- **1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine** (pKa ≈ 13–15)
- **2-tert-butyl-1,1,3,3-tetramethylguanidine** (pKa ≈ 13–15)

#### **Group C: Phosphazene superbases (pKa ≥25)**
- **N-[dimethylamino-ethylimino-[[tris(dimethylamino)-lambda5-phosphanylidene]amino]-lambda5-phosphanyl]-N-methylmethanamine** (pKa ≈ 25–40)

### Step 4: Justification

- **Groupings are strongly justified by pKa (conjugate acid) values, as documented in reputable physicochemical property databases (e.g., Handbook of Chemistry and Physics, Reaxys, SciFinder).**
- **The number of basic nitrogens** and **direct references to superbase families** further support this separation: only the phosphazene achieves the highest basicities by design; guanidines and bicyclic amidines plateau at lower (but still high) pKa.

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## **Result Table**

| Substance                                                                 | Group | Justifying pKa (Conjugate Acid)     | Nitrogen Sites |
|----------------------------------------------------------------------------|-------|--------------------------------------|----------------|
| 1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine                   |  A    | 13–15 (estimated, database analogs) |        2       |
| 2-tert-butyl-1,1,3,3-tetramethylguanidine                                 |  A    | 13–15 (database, guanidine analogs) |        3       |
| N-[dimethylamino...phosphanyl]-N-methylmethanamine (phosphazene)          |  C    | 25–40 (database-measured)           |      6–8       |

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### **Summary**
**The three bases clearly separate into two groups (A and C) based on pKa (quantitative, database-supported) of their conjugate acids:**  
- **Group A:** Moderately strong, non-superbase nitrogen organic bases (1 & 2).
- **Group C:** Phosphazene superbases (3).

**There is no clear candidate for an intermediate or Group B (pKa 17–24), so only two groups are strictly necessary.**

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If you wish to use a different property or want more granular groupings, let me know your preferred classification principle!