Let's systematically classify the three candidate substances, primarily using **quantitative physicochemical property data**, following your guidelines. I will select **up to three groups**, but I will consider justifying ONE group if appropriate.  

I'll focus on key properties relevant for organic bases and polar aprotic/hydrogen-bonding capabilities, such as:

1. **Basicity (quantified by pKa of the conjugate acid)**
2. **Polarity (quantified by dielectric constant, or calculated logP)**
3. **Proton donor/acceptor count (quantified by formal H-bond donors/acceptors)**
4. **Molecular size/volatility (boiling points, often linked to bulkiness and application in synthesis)**

## Substances and Data Gathering

### 1. **2-tert-butyl-1,1,3,3-tetramethylguanidine**

- **pKa (conjugate acid):** Very high, typical values: ~13-14 (some sources up to 16-17). Classified as a **superbase**, very strong organic base.
- **H-bond donors:** 0  
- **H-bond acceptors:** multiple (at least 1-2 N atoms)
- **Boiling point:** ~180-200°C (moderately high)
- **logP:** Moderate, due to alkyl groups, but not extremely hydrophobic

### 2. **N-[dimethylamino-ethylimino-[[tris(dimethylamino)-λ5-phosphanylidene]amino]-λ5-phosphanyl]-N-methylmethanamine**  
(also known as **P2-Et Base** or **Schlosser's base family**)

- **pKa (conjugate acid):** Extremely high, typically reported **>30** (among the strongest non-ionic organic bases)
- **H-bond donors:** 0  
- **H-bond acceptors:** many (multiple N atoms, phosphorus centers)
- **Boiling point:** Typically high, but less data (often used in solution)
- **logP:** Expected to be high due to extensive alkyl substitution

### 3. **1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine**  
(likely a tertiary amine, bicyclic system)

- **pKa (conjugate acid):** Estimated around **10-11** (similar bicyclic amidine/guanidine frameworks)
- **H-bond donors:** 0 
- **H-bond acceptors:** 2+ (nitrogen atoms)
- **Boiling point:** Not widely reported, but expected to be moderate (~>150°C)
- **logP:** Moderate to low

---

## Classification

### [1] **By Basicity (pKa of conjugate acid, Quantitative Ranges):**
#### Category boundaries (for organic bases):
- **Extreme/superbase:** pKa > 20
- **Strong base:** pKa 10-20
- **Moderate/weak base:** pKa < 10

#### Classified:
- **P2 Base:** pKa > 30 → **Extreme/Superbase**
- **2-tert-butyl-1,1,3,3-tetramethylguanidine:** pKa 13-16 → **Strong base**
- **1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine:** pKa ~10-11 → **Strong base**

### [2] **By H-bond Donor Ability (Number of donors):**
- All THREE have **0 H-bond donors** (all are tertiary amines/guanidines, no N—H)
    - This places **all substances in a single group**: **No H-bond Donors**

### [3] **By Polarity (Approximated by H-bond acceptors and structure):**
- All are **polar aprotic** molecules (have multiple acceptors, no donors).
- Dielectric constants may vary but all are much less than water; do not split the group usefully.

### [4] **By Hydrogen Bond Acceptors (number of N, P, significant atoms):**
- **2-tert-butyl-1,1,3,3-tetramethylguanidine:** Multiple N (typically 2-3)
- **P2 Base:** Multiple N and P (5+ acceptors)
- **1-methyl...pyrimidine:** 2 N

These values differ numerically but all are in the "multiple acceptor" category, which does not provide sufficient justification for splitting >1 group unless a boundary is imposed (e.g., >3 acceptors).

---

## **Final Group Assignment [Justification Required]:**

### **ONE GROUP Justification**
- **All substances meet the criteria for "strong, non-hydrogen-bond-donating, organic superbase/strong base"— as quantitatively indicated by:**
   - **pKa values >10**
   - **Zero H-bond donors**
   - **Multiple H-bond acceptors**
- **No property among those listed splits them unambiguously into two or three meaningful *quantitative* subgroups using conventional physicochemical database divisions.**
    - Only the "superbase" category (pKa > 20) includes the P2 Base, while the others are just below this cutoff, but that's a single exception.

**THEREFORE: It is chemically most rigorous and justifiable (by pKa, donor/acceptor, and polarity) to place ALL THREE in a SINGLE GROUP.**

---

## **Summary Table:**

| Substance                                                     | pKa (conjugate acid) | H-bond donors | H-bond acceptors | Category      |
|---------------------------------------------------------------|----------------------|---------------|------------------|--------------|
| 2-tert-butyl-1,1,3,3-tetramethylguanidine                     | ~13–16               | 0             | 2–3              | Single Group |
| N-[dimethylamino-...phosphanyl]-N-methylmethanamine (P2 Base) | >30                  | 0             | 5+               | Single Group |
| 1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine       | ~10–11               | 0             | 2                | Single Group |

---

### **Final Classification:**
> **All three substances are classified into a SINGLE GROUP:**
> - **Strong/Exceptional Organic Bases with Multiple H-Bond Acceptors and No H-Bond Donors**
> - This is justified by clearly high, quantifiable pKa values (all >10), zero donor counts, and similar acceptor counts, with no database-valid divisions that would define a finer grouping.  

If a superbase/strong base threshold (pKa > 20) is strictly imposed, P2 could be alone. However, conventional grouping for synthetic applications does not do this unless specifically needed. **Thus, ONE GROUP is justified.**